{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  In Depth: Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Up until now, we have been looking in depth at supervised learning estimators: those estimators that predict labels based on labeled training data.\n",
    "Here we begin looking at several unsupervised estimators, which can highlight interesting aspects of the data without reference to any known labels.\n",
    "\n",
    "In this chapter we will explore what is perhaps one of the most broadly used unsupervised algorithms, principal component analysis (PCA).\n",
    "PCA is fundamentally a dimensionality reduction algorithm, but it can also be useful as a tool for visualization, noise filtering, feature extraction and engineering, and much more.\n",
    "After a brief conceptual discussion of the PCA algorithm, we will explore a couple examples of these further applications.\n",
    "\n",
    "We begin with the standard imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Introducing Principal Component Analysis\n",
    "\n",
    "Principal component analysis is a fast and flexible unsupervised method for dimensionality reduction in data, which we saw briefly in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb).\n",
    "Its behavior is easiest to visualize by looking at a two-dimensional dataset.\n",
    "Consider these 200 points (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "By eye, it is clear that there is a nearly linear relationship between the *x* and *y* variables.\n",
    "This is reminiscent of the linear regression data we explored in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), but the problem setting here is slightly different: rather than attempting to *predict* the *y* values from the *x* values, the unsupervised learning problem attempts to learn about the *relationship* between the *x* and *y* values.\n",
    "\n",
    "In principal component analysis, this relationship is quantified by finding a list of the *principal axes* in the data, and using those axes to describe the dataset.\n",
    "Using Scikit-Learn's `PCA` estimator, we can compute this as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The fit learns some quantities from the data, most importantly the components and explained variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.94446029 -0.32862557]\n",
      " [-0.32862557  0.94446029]]\n"
     ]
    }
   ],
   "source": [
    "print(pca.components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.7625315 0.0184779]\n"
     ]
    }
   ],
   "source": [
    "print(pca.explained_variance_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To see what these numbers mean, let's visualize them as vectors over the input data, using the components to define the direction of the vector and the explained variance to define the squared length of the vector (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_vector(v0, v1, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    arrowprops=dict(arrowstyle='->', linewidth=2,\n",
    "                    shrinkA=0, shrinkB=0)\n",
    "    ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
    "\n",
    "# plot data\n",
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    draw_vector(pca.mean_, pca.mean_ + v)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "These vectors represent the principal axes of the data, and the length of each vector is an indication of how \"important\" that axis is in describing the distribution of the data—more precisely, it is a measure of the variance of the data when projected onto that axis.\n",
    "The projection of each data point onto the principal axes are the principal components of the data.\n",
    "\n",
    "If we plot these principal components beside the original data, we see the plots shown in the following figure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "![](images/05.09-PCA-rotation.png)\n",
    "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Principal-Components-Rotation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This transformation from data axes to principal axes is an *affine transformation*, which means it is composed of a translation, rotation, and uniform scaling.\n",
    "\n",
    "While this algorithm to find principal components may seem like just a mathematical curiosity, it turns out to have very far-reaching applications in the world of machine learning and data exploration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### PCA as Dimensionality Reduction\n",
    "\n",
    "Using PCA for dimensionality reduction involves zeroing out one or more of the smallest principal components, resulting in a lower-dimensional projection of the data that preserves the maximal data variance.\n",
    "\n",
    "Here is an example of using PCA as a dimensionality reduction transform:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original shape:    (200, 2)\n",
      "transformed shape: (200, 1)\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)\n",
    "X_pca = pca.transform(X)\n",
    "print(\"original shape:   \", X.shape)\n",
    "print(\"transformed shape:\", X_pca.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The transformed data has been reduced to a single dimension.\n",
    "To understand the effect of this dimensionality reduction, we can perform the inverse transform of this reduced data and plot it along with the original data (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = pca.inverse_transform(X_pca)\n",
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The light points are the original data, while the dark points are the projected version.\n",
    "This makes clear what a PCA dimensionality reduction means: the information along the least important principal axis or axes is removed, leaving only the component(s) of the data with the highest variance.\n",
    "The fraction of variance that is cut out (proportional to the spread of points about the line formed in the preceding figure) is roughly a measure of how much \"information\" is discarded in this reduction of dimensionality.\n",
    "\n",
    "This reduced-dimension dataset is in some senses \"good enough\" to encode the most important relationships between the points: despite reducing the number of data features by 50%, the overall relationships between the data points are mostly preserved."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### PCA for Visualization: Handwritten Digits\n",
    "\n",
    "The usefulness of dimensionality reduction may not be entirely apparent in only two dimensions, but it becomes clear when looking at high-dimensional data.\n",
    "To see this, let's take a quick look at the application of PCA to the digits dataset we worked with in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb).\n",
    "\n",
    "We'll start by loading the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Recall that the digits dataset consists of 8 × 8–pixel images, meaning that they are 64-dimensional.\n",
    "To gain some intuition into the relationships between these points, we can use PCA to project them into a more manageable number of dimensions, say two:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797, 2)\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(2)  # project from 64 to 2 dimensions\n",
    "projected = pca.fit_transform(digits.data)\n",
    "print(digits.data.shape)\n",
    "print(projected.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can now plot the first two principal components of each point to learn about the data, as seen in the following figure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(projected[:, 0], projected[:, 1],\n",
    "            c=digits.target, edgecolor='none', alpha=0.5,\n",
    "            cmap=plt.cm.get_cmap('rainbow', 10))\n",
    "plt.xlabel('component 1')\n",
    "plt.ylabel('component 2')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Recall what these components mean: the full data is a 64-dimensional point cloud, and these points are the projection of each data point along the directions with the largest variance.\n",
    "Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the data in two dimensions, and we have done this in an unsupervised manner—that is, without reference to the labels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### What Do the Components Mean?\n",
    "\n",
    "We can go a bit further here, and begin to ask what the reduced dimensions *mean*.\n",
    "This meaning can be understood in terms of combinations of basis vectors.\n",
    "For example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$:\n",
    "\n",
    "$$\n",
    "x = [x_1, x_2, x_3 \\cdots x_{64}]\n",
    "$$\n",
    "\n",
    "One way we can think about this is in terms of a pixel basis.\n",
    "That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image:\n",
    "\n",
    "$$\n",
    "{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n",
    "$$\n",
    "\n",
    "One way we might imagine reducing the dimensionality of this data is to zero out all but a few of these basis vectors.\n",
    "For example, if we use only the first eight pixels, we get an eight-dimensional projection of the data (the following figure). However, it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "![](images/05.09-digits-pixel-components.png)\n",
    "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Digits-Pixel-Components)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "The upper row of panels shows the individual pixels, and the lower row shows the cumulative contribution of these pixels to the construction of the image.\n",
    "Using only eight of the pixel-basis components, we can only construct a small portion of the 64-pixel image.\n",
    "Were we to continue this sequence and use all 64 pixels, we would recover the original image."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "But the pixel-wise representation is not the only choice of basis. We can also use other basis functions, which each contain some predefined contribution from each pixel, and write something like:\n",
    "\n",
    "$$\n",
    "image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n",
    "$$\n",
    "\n",
    "PCA can be thought of as a process of choosing optimal basis functions, such that adding together just the first few of them is enough to suitably reconstruct the bulk of the elements in the dataset.\n",
    "The principal components, which act as the low-dimensional representation of our data, are simply the coefficients that multiply each of the elements in this series.\n",
    "the following figure shows a similar depiction of reconstructing the same digit using the mean plus the first eight PCA basis functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "![](images/05.09-digits-pca-components.png)\n",
    "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Digits-PCA-Components)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Unlike the pixel basis, the PCA basis allows us to recover the salient features of the input image with just a mean, plus eight components!\n",
    "The amount of each pixel in each component is the corollary of the orientation of the vector in our two-dimensional example.\n",
    "This is the sense in which PCA provides a low-dimensional representation of the data: it discovers a set of basis functions that are more efficient than the native pixel basis of the input data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Choosing the Number of Components\n",
    "\n",
    "A vital part of using PCA in practice is the ability to estimate how many components are needed to describe the data.\n",
    "This can be determined by looking at the cumulative *explained variance ratio* as a function of the number of components (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA().fit(digits.data)\n",
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative explained variance');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This curve quantifies how much of the total, 64-dimensional variance is contained within the first $N$ components.\n",
    "For example, we see that with the digits data the first 10 components contain approximately 75% of the variance, while you need around 50 components to describe close to 100% of the variance.\n",
    "\n",
    "This tells us that our 2-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance.  Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in its features."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## PCA as Noise Filtering\n",
    "\n",
    "PCA can also be used as a filtering approach for noisy data.\n",
    "The idea is this: any components with variance much larger than the effect of the noise should be relatively unaffected by the noise.\n",
    "So, if you reconstruct the data using just the largest subset of principal components, you should be preferentially keeping the signal and throwing out the noise.\n",
    "\n",
    "Let's see how this looks with the digits data.\n",
    "First we will plot several of the input noise-free input samples (the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n",
    "                             subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                             gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8),\n",
    "                  cmap='binary', interpolation='nearest',\n",
    "                  clim=(0, 16))\n",
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's add some random noise to create a noisy dataset, and replot it (the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.609434159508863"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.default_rng(42)\n",
    "rng.normal(10, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8hx9+kGO89/D444/L/WfNmuXmOXPmdHP1MzfTRQ2hG6QPBXXTqZlZmTJl3PzTTz91c6/IIpMqkAhdM9SN94r3eXz99ddy/wsvvDDV/CHjxo1z89DrV61a1c23bNkix4RuRva0bt3azdVNt7t375ZzzZ07182bNm0qx7Rs2TKRqRvPlVDxiXrtk046yc3vv/9+OdeIESPcvGTJknKM2qbOa/6yAwAAosZiBwAARI3FDgAAiBqLHQAAEDUWOwAAIGosdgAAQNSyLD33SsNDvbGUW265xc0HDBggx6hS5xo1asgxqi9HqMzTM2XKFLntvPPOc3NV8rtixYpUr20WLkNU/bTSCJX8qxJ6VQrcv3//1K+vyqCVUJmsVyof6sOieqd8/PHHbv6Pf/xDzlWgQAE3nzhxohyjHkWgjtHruda3b185v/r8VDnx3XffLedS/bRC1M83VHruPeKiVatWcn/1+IupU6e6+fXXXy/nUmXIO3bskGNCJbkHK3RNUiXm6hxVeUioF9KaNWvcXPWcu+mmmxJZv3795Pzvv/++m7do0cLN1WNIzMz279/v5nPmzJFjrr32WjcPlZ6npXo4LliwwM1Vrycz/Tsn9EgFT9pHlJQuXVpu80rbzfT3fMKECXIudW1Sn62ZfvyEWh/wlx0AABA1FjsAACBqLHYAAEDUWOwAAICosdgBAABRy7IayxNqBNqpUyc3VxUPIYMGDXJz1WDNzKxZs2apX8ej7n43041DP/roo9Svo5omhqpgvMaFoYov7073TZs2yf1fe+01N1eNKkPVSqoh5xFH6HV248aN5TbP5s2bE1n58uVTzWFm1rFjRze/5ppr5JhQU1pl3759qfb3jkU1BjTTlQ3vvvuum5977rlyrieeeMLNQ006Q1VXSvXq1RPZyy+/LPdX58+iRYvcXDV/NdMVKqHv1KpVqxJZqKGqp1y5cnJbtWrV3FxVJZUoUULO1aFDBzcfPny4HKMqXdIc4wMPPCC3zZ8/383Hjh3r5rt27ZJz9ejRw80rV64ceHeHRqhqVjUQVtWY6vtpFm6ErKSt2vWqpS666CK5vzrnvMrKrDz11FNuHmoyrRr40ggUAAD8T2KxAwAAosZiBwAARI3FDgAAiBqLHQAAELVsVWOFDBkyxM2bNm3q5jfffLOc68CBA25esmRJOaZw4cKBd+dbvHhxIlNVHWZ+Hxgzs9tuu83NQ3e0L1++3M2zcxzKiSeeeFBZJlUpEerdovz6669ufumll6aeSylWrFgiU/1nzMxKlSrl5l999ZWbN2jQQM7Vtm1bNw9VuhyKz/b//u//Uo85lP2AihQpIrf99ttvqefzKgDPOeccuX++fPncXPXFURU7Zrrfk1chlklVJipe1U6oIlFdR3fu3OnmoX6Be/bscfPOnTvLMcWLF5fbPBs2bEhkob5KqvJRVRLmzZtXzqV+VqGefap/W1pHH3203Kaq0VQV08aNG+Vcqso5VLHoVfuFeoyFfk95VNWsur6G3mvDhg3dPPQ5pe3bx192AABA1FjsAACAqLHYAQAAUWOxAwAAosZiBwAARI3FDgAAiFqWpecLFy5MZH/++WfqF6pUqZKbh0qQ77jjDjcPlYSqxoyh5qVec7tQ+ey8efPcXJWSHnvssXIu1czsX02VsJrpRnWqOWBIdkrMVbm6snTp0kRWs2bN1K+bM2dON1fNCc3MGjVq5OahJnxnnHFGujfmCDXinDx5spuvWbPmn37dTKGy8GXLlrn5cccdJ8d07dr1n35PZmaPPfZY6jGffPKJm6sSWjOz2rVrJzLVgNDML1EOlS17192QPHnyyG1dunRxc/UoAjP9GapjDJWZe9T5O3jwYDcPNc/99ttv3Vw9QsPMbPz48W5epkwZOcazZMkSuW3cuHFuftddd7l5dhpohh6B0KRJk0QWOke9R7CErqPq8Szq9/bMmTPlXOqxLaHPQzVaVfjLDgAAiBqLHQAAEDUWOwAAIGosdgAAQNRY7AAAgKhlWY3lVR2EeJVNZma9evVyc3XXv5m+27tgwYKp3pNZ+C70XLlyJbKpU6fK/VUjx59++snNvYZsmVTlTKiaRzVBTEM1WTXTVRo///yzm1erVk3OVbRoUTefMmWKHFOnTp1EphoEmvlNTUPzq0qiXbt2ufnzzz8v51IVAaFqqQkTJshtHq9RZ6gR59y5c93ca5hqFm6ol52GiapCRH0/zPyqlty5c8v9VXXnfffd5+YXXnihnKtZs2Zy23+KqgBU155QZZf6LqgGqGZm/fr1c/MWLVq4+f79+xNZ6Lxq3ry5m48ePdrNVZWtWfbO0ZNPPtnNQ78nPKEGrOq86t69u5t36NBBzqUquEIVdWmlrWBVVVcvvPCCm4fOB7UO+P777+WYtOcof9kBAABRY7EDAACixmIHAABEjcUOAACIGosdAAAQNRY7AAAgalmWnqf15Zdfurlq9PX222/LubZu3erm2Sk9D/Hew5VXXin3VyWbu3fvdvNXXnlFzqVKClXJtplfQhwq6/UUKFBAbrvzzjvdvH///m4eem3VNLVly5ZyjNeIVL0nM/9YLrjgArn/Pffc4+aqAemmTZvkXK1atXLzUHn59OnT3bxQoUJu7pXEh0rPVYm5Kk8OPTpAlaN6TQMzqYa4IVWrVk1kX331ldy/QoUKqea///775bZffvnFzffu3SvHhBrperZv357IQtexjRs3uvkDDzyQKjfTj5l46qmn5BjVwFeVZnuPG1C/C8z09Sc75+iMGTPcXDU0NtOPNQk1VL399tsTWe/eveX+XoNiM7P27du7eegz/E8JXdvVNaBz585uHvrOfv31125er149OUZ9p9X74i87AAAgaix2AABA1FjsAACAqLHYAQAAUWOxAwAAopbxV6CLWtqmaP/tTjvttEQW0zFyfIe/vx9j7MdnFtcxxn58Zpyjh7vYj8/MP8bgYgcAAOBwx39jAQCAqLHYAQAAUWOxAwAAohZsF/G/cNNSTMfI8R3+uPnz8Bb78Zlxjh7uYj8+M/8Ys+yN5fUFCvUdUjIyMtw8NJf3hs3M+vTpk/r1Qx+m9zqql5eZ7odyzDHHuLk6djOzXLlyufnPP/8sx3i9fLZt2yb3945v3bp1cv8PP/zQzTt27OjmoXvcJ06c6Oaqv5iZ2WWXXZbI0n5+IQMHDnRz1bNq8uTJcq6ePXu6+VVXXSXHTJ061c3r16/v5kcemfyaVq9eXc6vjBgxws3feecdOeaKK65w8+bNm8sxqudT2s9wypQpcv8WLVq4ueqxo37mZmavvfaam48ZM0aO8b7rq1atkvunvY6uX7/ezVu3bu3ma9askXOpHoNeP6usqM/QOx9DPdLUtoceesjNx40bJ+dq06aNm/ft21eOmT17tpsfddRRcky5cuUSWeHCheX+K1ascPNBgwa5+R133CHnqlKlityWRtrv4EcffST3HzJkyEHPY2a2evXq1HONHj1ajjnuuOPcXPVd47+xAABA1FjsAACAqLHYAQAAUcvynp2FCxcmshIlSsj977//fjcvXbr0Qc+f6cwzz3TzJUuWyDF79+5187T/P63uxTAzGzp0qJsff/zxbh76eeXOndvN8+TJI8eUL18+kYX+L7Zr166JrHHjxnJ/dW+Oul9A/R+pmdmOHTvc/Mcff5RjvHslKlSoIPffsGFDIps7d67cf9q0aW5etmxZN1fHbWb222+/uXm1atXkmD179ri5+gxXrlyZyLJzz06dOnXc/IYbbpBjHnnkETdX9+UcSjVr1kw95vTTT3fzs846S45p27atm5944olyTOgeGc8555yTyLzzNtNbb73l5vXq1XPzL774Qs6lrrF169aVY9Ly7ivLjmOPPdbNW7ZsKcf069fPzd999105Rv0OCV1HvftzQp/hsGHD3Pyzzz5LlZuZPfjgg25esWJFOSZ0DfJs2bIlkanzzczsqaeecvMePXq4ufpszcxuvfVWN/d+12VS56/6DPnLDgAAiBqLHQAAEDUWOwAAIGosdgAAQNRY7AAAgKix2AEAAFHLsl7Qa82wefNmPaEoQXz66afdPFQCrR7x/tNPP8kxqrxt//79cownVBKvyuuPPvpoNy9UqJCcSz2ePGfOnHLM2LFjE5n3KPNM3mPT8+bNK/c/9dRT3VyVFIYe6z9q1Cg3v/baa+WY9u3bJ7JQSaj3M1TtBMzM2rVrJ7el1b17dzdXrRmyw2ufkR2XXHKJm4ceCX/vvfe6ea9eveSYtO07zPz2Ex988IHcX52/qjXCt99+K+dS353QIy68kmP1+Hoz/xET6nEcZmbPPvusm69du9bN1eMMQmNCtm/fnmr/5cuXJ7JTTjkl9etefPHFbq5a8ZiZPfbYY24eeqRCdhw4cCCRhX62jz/+uJurVjKhRx3UqlXLzZ9//nk5Jm3peZEiRVLtrx7zcPnll7v5lVdeKedSPxP1O8cs/aMT+MsOAACIGosdAAAQNRY7AAAgaix2AABA1FjsAACAqGWre1uxYsXktt9//91/IVGlVbRoUTnXXXfd5eahaqxQ1Y7y9ttvJzJVRWTmV0OZ6YqIUNPLQYMGZfHukho1apTIQg3pQpVXHnWHf40aNdy8ePHicq5Q1ZXiVeGFqjEyMjISWeiYly1b5uZVq1Z1c9VA00xXHqkGoWbhasaDFaq+ue2229xcVUSGmmSqBn0nnHCCHKOuASHjx49PZDfffLPcX30Hzz//fDd/+eWX5VyqGs1r3pnJ+y6kvfYMGTIk1f5mZq+++qqbq6pOM7NKlSqlfp3Q+etJW3l1xhlnuLmqplu1alWq+c309crM7M8//0w9n9eQ17v2ZNq4caObe42ZzcwuvfRSOde6devcPHQcK1askNs8S5cuPagsU/369d387LPPdnOvsjuT+j2oqrTMzHbt2iW3efjLDgAAiBqLHQAAEDUWOwAAIGosdgAAQNRY7AAAgKhlqxpr06ZNctvMmTPdXN253bp1azlX4cKF3VzdmR56b6G+NVWqVElkqurBzGzevHluPnLkSDlGqVmzZuoxXv+vUDWWJ1TRpvqVqcq5UI+SLVu2uHna3kqhaixv23fffSf3V1VXSqhPWrdu3dw81H8r9N48XkVEqO/NsGHD3DxPnjxuHqqS8CpQzMIVmdmRI0eORKZ60JmZlSlTJtX8f/zxh9yWK1euVHMdKqGfu+qHdvvtt7u56ntmpiu1du/eLceULFnSzUPX/r9755135LZt27a5ealSpVLlZmazZ89281DvscWLF7v5EUfof/97FWezZs2S+6vroqrODVVY/vXXX27+xRdfyDEVKlRIZKF+b941JV++fHJ/dR1T7zVE9ZVcv369HBOqCPXwlx0AABA1FjsAACBqLHYAAEDUWOwAAICosdgBAABRY7EDAACilq3S81AZd6FChdz8iiuucPMdO3bIuVTzN69pYCbVZC3UpK98+fKJbO/evXL/nTt3uvlnn33m5g0aNJBzvfLKK27+yCOPpBpz6qmnyv09Xvl6JtXATpWRq8aTZmZFihRx81C5+tVXX53IQp/fnDlzEplqNBiiPtfhw4fLMe3bt3fzyy+/XI7xzjczfYxeqfyMGTPk/Kr0UzXJ9H5+mXLnzu3mq1evlmPU8YV4pacHDhyQ+6tjnDx5spv37t1bztWzZ88s3l3S+++/n8hC36nt27cnMq+hbyZ1jVONMtXnZKbLeqdNmybHqEeFpPHSSy/JbapJpWpsOWbMGDmXauS6YMECOUY1eQ091sSjrm9musR8/vz5bj548GA5l2qKHXp0SfXq1eW2gxV6LEOogXBa6vfghAkT5JjQdcvDX3YAAEDUWOwAAICosdgBAABRY7EDAACixmIHAABELVvVWKHmY6px4AMPPODmy5Ytk3MVKFDAzc877zw5pn///m6u7r5XQo0y27Rp4+aVK1dO9RpmZs8884ybN23aVI655pprElmoWsmrlho0aJDcP9RAzzNgwAC5TTW38yquMn3//fepXj9t5dWIESPcXFWbhSoClEmTJsltF1xwQaq5MjIyEll2KiFUY80XXnhBjlEVQ9mpuErrxBNPlNtUE8J7773Xzb1mqpnuu+++VO/LzK9sC30Hf/jhh0Q2atQouf8tt9zi5qrZ8Mknnyzn2rdvn5tffPHFckyahp/K6NGjU48pXry4m6sqNDN9zVfNVEPSVmN5zUGzUqdOHTd/8cUX5RhVZRxqkJqWV/1csWJFuf+iRYvcfOrUqW6u1gbqtc38Jt2ZPv74YzfPnz+/m/OXHQAAEDUWOwAAIGosdgAAQNRY7AAAgKix2AEAAFFjsQMAAKKWZem5VwacM2dOuX+LFi3cXJUzhxpYdunSxc1VSbqZWY8ePdw8VBbqlQmnLQ82083tOnbsKMeoZnm7du1K/TpKu3btElmOHDnk/uvXr3fz9957z82PPFKfRup1QmX6XtPGUGmtR5UympndcMMNqeZSzW3NdEPKPn36yDHZObfSUA0IVSl36FEOqjx52LBhcsyNN96o35zgvecSJUrI/Rs3buzm6lEHIaHyWmXgwIGJrEmTJnJ/r/Q89B0YOnSom6vS82+++UbOpX6OoccjpPXll18msrVr18r9jzrqKDd/7rnn3Fxd183MKlSokMW7+9dZvny53PbGG2+4eeHChd382WeflXOpRy2o64+Z2QknnCC3eULXcU/37t3dfPr06W5+8803y7lUA9jatWvLMer7pn7X85cdAAAQNRY7AAAgaix2AABA1FjsAACAqLHYAQAAUcv4K3A7d6iC6XB02mmnJbKYjpHjO/z9/RhjPz6zuI4x9uMz4xw93MV+fGb+MQYXOwAAAIc7/hsLAABEjcUOAACIGosdAAAQteDzof8XblqK6Rg5vsMfN38e3mI/PjPO0cNd7Mdn5h9jls0wvEEzZsyQ+6seWKp/Sdu2beVcb731Vhbv7uCFPkzvGEO8PjBmZoMGDXLz0DGqPkmbNm2SY3bv3p3Itm7dKvevWrVqIsuVK5fcPyMjw81bt27t5u+8846cS6lXr57c9sorrySyHTt2yP3/+OOPRLZo0SK5f8+ePd184sSJbv7hhx/KuQ4cOODmt9xyixzzyy+/pJqrWLFiB72vmdnevXvdfMuWLW5+xhlnyLmWLFni5tWrV5djlNB3cOPGjYlMnW9mZrfeequbq55ooT5BnTp1cvPQOeoJHZ93XTz22GPl/qoX3L59+9xcfbZmZp988ombq35EZmbly5d38zVr1ri5dw0NfQdV3yjvu2xm9thjj8m5Xn31VTe/6aab5Bgl7e8J9V0zMxs9erSbV6tWzc1HjRol53rmmWfcPNSDz+sxeCh/D6o+Zrfddpub58uXT8519913u7nqgWdmVrZsWTdX11f+GwsAAESNxQ4AAIgaix0AABA1FjsAACBqWd6gPG/evES2bNkyub+6ybNFixZu/vDDD8u51I2yoYc+Dx061M1DN195N79+8cUXcv+VK1e6+YgRI1LlZmavvfaam19xxRVyTNeuXRPZlVdeKfcP3YzsUTeTX3bZZW7+9ttvy7nUzdkDBw6UY44++uhEFrpB2bvR8+eff5b7lytXzs2bNGkix6T14osvym3qZlJ186B3c23oO6Bu8lQ3AYaomwqXLl0qx6gbMEO8m5Hvueceub/6Ds6aNcvN1Y29ZmY333yzm7/88styzA033CC3eT7++ONE1q5dO7n/t99+m2r+s846S26rWbOmm4fO91ARimfdunWJrGDBgnL/xx9/3M3Vjdm1atWSc6W9sTa7vBu6169fL/dfvHixm19//fVu3rlz59TvqVKlSqnHKO+++24iUzd/m5mNHTvWzdXN56owxExfT7ybrDM9++yzbl6/fn035y87AAAgaix2AABA1FjsAACAqLHYAQAAUWOxAwAAosZiBwAARC3L0vO6deseVJapSpUqbq76SYWocvW1a9fKMR07dnTzUE+QAgUKJLKGDRvK/UNl6Z7+/fvLbR06dHDzUOm514MrbSO3cePGyW1ff/21m//6669uPmHCBDnX+PHjU70vxeudlCl37tyJTPXwMQv37PFMmTJFbtu5c6ebh8qKD4VQ6bn6bCtXruzmoRLrY445Jt0by6bNmzcnspYtW8r9BwwY4Oaq15xXVpuV7PT/UrzriSqdDbn22mvdfOTIkXKMKgH/6KOP5BivP52Z2amnnurmu3btSmShc0ddp1WPP3XcZuHvghJ6fEqaMfv375f7q+NX/dtuvPFGOVffvn3dXD0OxCz8uAWP9yiCDz74QO7vXXfNdG8q9XsltG316tVyjOrBpX4X8pcdAAAQNRY7AAAgaix2AABA1FjsAACAqLHYAQAAUcuyGsvj3XmfKWfOnNl+M383efJkNw9V0xQpUiT160yaNCmRnXTSSXL/Ll26uLmqEOnRo4ecq1ChQm7+0ksvyTGhpp8H66uvvko9RjUHVM1fzfRxqCq07PCaVXoVdtl1zTXXyG2qEk01QDUze/755//p93TEEfrfKbt373Zz1XxRVZSZmb3wwgvp3piZbdiwIfUY7z2r6r+QmTNnuvmjjz4qx3Tq1MnN9+zZI8eULFky1fvyvudly5aV+9erV8/NVdXVtm3b5FyqUWaoqrR9+/Zurho2elW4oQpR1dhX/W4pXbq0nEtVH4YqIlUl0d69e+UY7z03btxY7n/KKae4eb9+/dy8W7ducq42bdrIbUra38X58+dPZKFztHv37m6uGgEXL15czqUaN5cvX16OSYu/7AAAgKix2AEAAFFjsQMAAKLGYgcAAESNxQ4AAIhatqqx3n//fbltyZIlqeaaPXu23KaqnipUqCDHqD4wIaqfjvLNN9+4+aeffurmJ5xwgpxLVe1UrVpVjsmTJ0/g3SX98MMPiSzU32zevHlurnqeTJ8+Xc6l+r0cymos7zMPVRGpnkT33nuvm4f6KnXt2tXN586dK8eoihbF66VTsWJFub/qO6QMHjw49bZQPyJVOfPTTz/JMb///nsiK1GihNxfVVepz/CZZ56RcxUtWtTNs9NzSfGqmx544AG5vzp/hg4d6uaqushM90iqUaOGHHMo/Pbbb3LbI4884uaqivLDDz+Uc23ZssXNQ/3xTj75ZDcPVZCFKq885557rpvPmjXLzUMVsupczMjISPWeQryfsbq+melqaVWpGOqNpSq11O8cM30dVWsA/rIDAACixmIHAABEjcUOAACIGosdAAAQNRY7AAAgaix2AABA1LIsPfdKQkMlmaqxpVK/fn25rUGDBm5+9913p3qNQ02V+6kS81CjxauvvtrNzzjjDDkmbUmsVwq4f/9+uX/hwoXd/Msvv3TzypUry7lUGXuo4Z56nUNFlcTWqVPHzZ944gk516uvvurmoWNQjfJU2atXZr5p0yY5v2riqB7Z0LlzZzmXKvG+9dZb5ZjsNA/1yutDzQ9Vw8i1a9e6+Z133innOu+889w89Bl6DW5DDWN79eqVyFSDTjOzUqVKufnZZ5/t5qFHOahS5zlz5sgx2Wmo/HeNGjVKPWbYsGFurh5hYWY2cOBAN//HP/4hx1x00UVuHmo86ZVB33777XJ/7zM304++UI1DzfTvkNWrV8sxaR8t0KxZs1T7lytXzs3VtX379u1yrurVq7t56BEeqsRd/X7kLzsAACBqLHYAAEDUWOwAAICosdgBAABRY7EDAACilmU1ltd0cuPGjXL/tJVC559/fqr9zczKlCkjty1evDj1fMuXL09koTvjjz/+eDcfNWqUmzds2FDOpZqZhZrOLVq0SG7zeBVRoUagSqhCTMlOM0Wv2u1QNmVUVX6qwWuIqoZ4/fXX5ZhJkyalfp2/y5s3r9ymKvzUd+3hhx+Wc6mKh1q1agXeXXqqAlBRTQVV88UQ1ej1gw8+kGMuueSSVK/hVV6pijIzXUmjvgcrVqyQc7Vs2dLNQ00WVVPKmjVryjFp9O/f38179OiRei5VXRn6Do4ZM8bNQ41AR44cmchGjBgh91dVkSeddJKbq8pHM7P77rvPzUO/p+bPn5/IcuTIIff3bNu2TW5TFZkfffSRm4eu4QsWLHDztE26zfRnyF92AABA1FjsAACAqLHYAQAAUWOxAwAAosZiBwAARI3FDgAAiFqWpeeem266SW7r1q2bm6vmmar5oplufhYqYVOlkaGSwi1btiQyrxw901NPPeXmqnT5xx9/lHOpxoWzZ8+WY7yfS758+eT+acvM1WfVtm1bN7/++uvlXOozVOWiZn4TwlCZrCf0M/cep2Bm1qpVKzd/8skn5VylS5d2882bN8sxoSasB+uNN96Q29T3c8eOHW5esGBBOdfu3bvdfMKECYF3l97QoUMTWaiR5PDhw91clcSHvv9K2sdihF7Da3AZam555ZVXuvnJJ5+c6j2ZmTVv3tzNc+XKJceo96aO0Wv+qEqQzczuvfdeN1+4cKGbT5s2Tc6lyqOffvppOWbGjBluXqBAATnG+67v2bNH7u+Vfpvp3xNNmzaVcykzZ86U2yZPnpzI1HmlhBp7FytWzM3r1at30O8nk2om/dxzz8kx+fPnd/MqVaq4OX/ZAQAAUWOxAwAAosZiBwAARI3FDgAAiBqLHQAAELWMvwKlTdmpYPhv5jXji+kYOb7D39+PMfbjM4vrGGM/PjPO0cNd7Mdn5h9jcLEDAABwuOO/sQAAQNRY7AAAgKix2AEAAFFjsQMAAKLGYgcAAETt/wHx+xg6wZWVtAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.default_rng(42)\n",
    "noisy = rng.normal(digits.data, 4)\n",
    "plot_digits(noisy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The visualization makes the presence of this random noise clear.\n",
    "Let's train a PCA model on the noisy data, requesting that the projection preserve 50% of the variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.50).fit(noisy)\n",
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Here 50% of the variance amounts to 12 principal components, out of the 64 original features.\n",
    "Now we compute these components, and then use the inverse of the transform to reconstruct the filtered digits; the following figure shows the result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = pca.transform(noisy)\n",
    "filtered = pca.inverse_transform(components)\n",
    "plot_digits(filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This signal preserving/noise filtering property makes PCA a very useful feature selection routine—for example, rather than training a classifier on very high-dimensional data, you might instead train the classifier on the lower-dimensional principal component representation, which will automatically serve to filter out random noise in the inputs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Example: Eigenfaces\n",
    "\n",
    "Earlier we explored an example of using a PCA projection as a feature selector for facial recognition with a support vector machine (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n",
    "Here we will take a look back and explore a bit more of what went into that.\n",
    "Recall that we were using the Labeled Faces in the Wild (LFW) dataset made available through Scikit-Learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Ariel Sharon' 'Colin Powell' 'Donald Rumsfeld' 'George W Bush'\n",
      " 'Gerhard Schroeder' 'Hugo Chavez' 'Junichiro Koizumi' 'Tony Blair']\n",
      "(1348, 62, 47)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_lfw_people\n",
    "faces = fetch_lfw_people(min_faces_per_person=60)\n",
    "print(faces.target_names)\n",
    "print(faces.images.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's take a look at the principal axes that span this dataset.\n",
    "Because this is a large dataset, we will use the `\"random\"` eigensolver in the `PCA` estimator: it uses a randomized method to approximate the first $N$ principal components more quickly than the standard approach, at the expense of some accuracy. This trade-off can be useful for high-dimensional data (here, a dimensionality of nearly 3,000).\n",
    "We will take a look at the first 150 components:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=150, random_state=42, svd_solver='randomized')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(150, svd_solver='randomized', random_state=42)\n",
    "pca.fit(faces.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In this case, it can be interesting to visualize the images associated with the first several principal components (these components are technically known as *eigenvectors*,\n",
    "so these types of images are often called *eigenfaces*; as you can see in the following figure, they are as creepy as they sound):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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t1qIHoZA65OcGDXalm87EjHcZcYlEPOk8U/mcnPKzz/ua4buICmBi2ivRmeT1XxsvrcNn8P4LB0I70F7OFcn7PENRSn52jW8Zasy9VZjfui3z2kCMfEt97KPX/VlmDZArlLQH6L5/9tniADiF15kx7ijCs97Bxkybzr2wtl6BBr9mCDmyMFGTjLbRCKhn6vcR/2tGn8h+PdTPkboVhviOKd4NiXIMTBct9xBidxDynKVkbz/8mKSkLOuYXiWrEcOpKL+ilAJbLJMwySDVUiiHnwunXiiPDWc2z6ydEQxl1kqR9J7TshviJLZ/v2xEv3YM0wAXCN7Vw7e2CLc3/vr5xjAC2XNMJJfN/7bt9RDHz/b7vkMQXtq3bGwlmqT3ZETOGVi+KOfdzcEO7TunBkiCh9cCNl2vLxj9zWvL9nzaDI5+n61rPN8HDfrfIsP7VMC3oH1kxLuIX5w/cYIcObFSdaHOGyM/W3SnXePnhpH36atkNG3THM/9PVau7FhixOI9ri5iWNfPftYXV0ZaI8EMSRijeQv9Se7vhchqC9PzjViPWpsRNrxJhCTRNpbRMjwhNLWoyyhBCoZK1uIS+SHQ+5Xi4TtropHKG4dA/C8NvacXjDLdf4O5+jnZQ3/GQBeREpRy1u8ZZ2EyMfv3edvXFhN5zZbY3/a2XB8AWsgM88M2Q9+T9p7fN98jP8tctw6AMGDlYBfvvXcEZPTzanVTyEHXlTw5A8orbze9RCc33bp1vO6ItCdGep/Tl8hIXyfOov7JUKnApXp9hSwBQ4aELthnh9pmLtjiWAs4V9t6eIXAebvh570tSF5XdvtsFDL+Bvt550jVsuF7hWW/j4j7qP1LQ5Cl29z618dwGHX/AbyPgY3x1+/369bSiSapIRkvzdvGqX+hVG/vAEqA3TtKlkgnGvDomeQdwo3pTf7wzjntI35snqmx2JhmdUZ4bqD/augIAAjATUeTcKLk1RwSoyE6ewRgA/8r8fV5CvnWIQbXBYcw9HuaLzJ3a9Vu/ySb1PbBi6WdvDc2ZX+lPn/+rg/u2v1Lmr1Wy6hcQYwJS0gYc8Ia42dd5S+ujJIr1aAzdC9Gvy+7AKC1psZsIw/ynCosChHZTAXw3BAZOFjbDgyKshnGt1XJawbbMigAKCVT/XJ0CiXKoUXXZm82/JK7fo1YtB8tV7WFt3Su+KH1kahsppdGc5gsinjgpuXdrOSHu83SPpeiLEmLvHWog+V6Z0sOF/p5X34nhjtXjgBr3ThF8vdaO6Z+pVIYmZ9cW33/Jn2hzhI0GtqjI9YZ1LLNOb4UPX/tcM7T5nLNURP2PpWN+U2efZu33x7i9DwyQdibn1MqwfKeENBcIh2z377qLLKTYSjn73x4MZ9/67pXx6zUjS7FJtLs90AxyuCHGIbNPnh2J5vPeTZX1eCVW3/1PG+RYPfNL7CbXxthDBvDXTRy5+vlT0RnzHpDADxPNbwWiW7WclcxID97aTSUQGD5pqFA6BRpj9xi/MTYWtvIos8MF8QR6dZ593dy/DkY5OCHImL+5QJ1pPr7FB6XfsZnOCp0nj4nBKI2e3HLoHsHOU+DV72Y3YsgCI8EISVnva59SfuL81fa9crvGWths0UVVJ3RzZwcUswwNikCWzvHTuxdykS+zbV81rh/0fBngdI5t59T1ovqYRmBJZwngg1AzoCWAQGwpW4WCh32PUnolctRw/ZydNB/v+SCdYnwpZXSGAOY9bZcdx/RU6nuS5779t9idOXPUkon8FH1lzbwXgfv9D9v99kM8aYkUHO83wbrv3zvL3i1hqJ+IwQ6mfcKGDRols5tcgxs94YS5cs8SfRf2ODr4ShefOfVFznUXzjMNRqmwloA0Ly/eSU//KVB3IagUTYAjfifiyVtU0Jbxy+jWgsCrA1H9lvnV9Iy+3uqaCkAAJtUt4Fh9KFFQHRo9xHarYYfenhpjTWjepXhfrjdnuyimEZE+3yqZbO+dvn67es6J8jQTFZjOO323OGW8ZqQypfGMA3NQWd9gForE+/YGc1F13qtsuYa7Nsc/arp0Vqrnp/qmFoxIlbndr+P1Zmo7QwVYaTeMffewRqjZchINzj96uCazeG2Pas43dYFBjI0yuU1U/ZnX/d+sFwJVQn1QN7C9zpntRFbJbJ/cdTnHIFb7r8/awVN6QO5/rXtngkZp7L21JUsdo5c59i9eI3dHsqJUpjZFVhH2jW1OEbeWrC4TwMALwQMu/Flwx8z1QpquV6rs1fW/gtMQ9RKCEEnyCM3+zwSKl0k027iJYiaPFooNFZrhelgFwDsZdFBuvLn+eE2oos12/c29aWDplvsWTw9gXjwbMGY3pDwoScRvWFySDsQLaytKM7CFk4B2ObZ9xHva9Htt2wC02+C3mljQ+1eqVGVvwsq8JIGgjFU25/R0ABnmcHccTzE4Ksh4ii0J5sZNgKbeTUEle3Z4F87rPUQwtRGGUxY9CLWw4ZfrpeMMOe4TW5Go1YY1M1hIX/W+vKBT7/b0lxVRG3oxVT3y0Qs74lt3Gs45HwbCC4Ofun39wvXqX92THMZkrPUPWu6nCWRQp7db5uLbYqn/5NwkUqcAXV2WmmdIBWvoWhfM8Lgla8EI44MVZ5u9jLBlIDWo5OjKZ9cKzYoqZwH7X7butoGNdDvo1OltM5q6aIRFVPmujjfdDNoL/0DtGLZ7Sf5u3UGLkiFSrvuDbfrFaP/DNHg++rXatsbUlIqRn8XPRtLe4p/p6Kt2VuJzVKZsUUVAVmTpRatcKn8RRVrVLWWY1LV1o29Mw0dknvfngESY3TIRe1gfQ6cyeHqUgv9XPLHeOc+W8/zRcNfa1W1PnECekOdUyvTy+zt5JjU6G8kerUGuRloUSMDGjuc/r5dVP3CaWUVtNkT0rNIQYhFSFTuMLxSivM1Q6L+Ajp8ct0aN6o7b1yHHm7sy1ZeNcDPvOoGI1lHBsRks3mtsLq1nMs8n6dqClC/4b45d96/dylFjXEpBaU2dcBqmkMAWAoI63MjAd4MkpywqKg8x7W73t5gb+e4kcxeGrppLWAr1/jfMEIYUGtFzlarUejZ7KL1WoioJvMGhr1JqeCLn0PzJ9f4PHrqPom+B5AAkDEiHsyHnNeIHxAn5bY0j+zphlztIradIegPcL32UvX29wS2Z3NQKupuqmTfAdigAbUSilR3FTaGCWLP8u43DOMsbK2kycHoobHYoE0bpKO2vd4HO73D2pdikRMhxqN279MhSyxzbD1FncTYb4Jkcj664Mmh2lXL3OrwfnZeJK3l9nwVbM44OfP6+9s4hd3v9kETkfde56v0jtL+PfevuzHLBR8oqrYvsPJVXriXY49MZs8ibY0uQCka3BlTBUZ99r76/oX4OzI2AaAoJmqAS6hAj8xY27RU4ufu8UuTILmDTf1gtwFf8q57mBOFiAeiqSwbo/0+b4gup2mshfdV89hCKttOUIGpZpPDtD0KYNumkc1xyxAo2ljbZdHlZz1E/fLv75nF2wh9q/BnnWVo0MFmET55lkfo3ut1st/m9248ADYRPh9SVFdfNxtcX4vuEOZ/awVAR5IUwylrJBcD081srk2iVQ8POVxzeRYx6K1yVCbvrcbiRna394OuL4HsofX8fLgW4ZE4GGQUY2CtRPetVE/4GPaV8ighOLXvbU+tHr4ndKMqL2BTvWEdlVNaUvFzNxI7ZU/XIrnUl9eQRCAbsuUr8/0SN2Ab/W4RK3WATVtHsr9zkSRx/9qX3vPbjB/NKSF9FaTmZ7JBRlMfTVLOLBVNHPSIHLkYgI0zUmsrlWR1RAmWjDHai8RxJC89MoZpQK0jrHfwLNBlHelqAKCziCemfIOAz2vk0pcct/0Uv4S0bNaQoRp4AAppN40X+crPzjprKowzm71H17r7HGzTY28dfggkd9ydHbViQ3ItrEKbOsl6AKxu2vT85dnKfe/3SK1Q7oxcu/S3sGy/fHAt3VAq96QQW+o1kKq1qraKt/YbDb9AnNbCecphyX3knNtiYJJL7+nlmJFSbA1mWJxHFre8vx50tcJYKp2geTIwZiKN8x1DVg0+w0ky2c1jNjxpJDHrbtwEch37sY8ojHn5dS/9nlyflvjw4VkrSZw672gjMMy/zen3h2bjSPTXQ9/rruUrruu1a5WSLptoMRbnUH1FT+prH9OiMtcd1t5Z1esHtpFIrRXeWaRcYBjqK7UiWdIJKKUgdhUEktO0nkgwe4i0n+NaOOq/EfLryXPWZnVNGhRXOki3bW4isVqUmmG7MFb0/B0roenv1doO60LRhGyyivZMDfY514xtGZ/A6J7RCYt047M3m+XDuXT+geZ4uYRMDjQ1Cj0EyXvVFqPRjwCGpmAj1tOL02zm9IbxrRE/IIgJALQKI3rPhBRrp2bKSqbSVCt21U+pMc2frdNewjxlIlDHhFqhZD3vHTwb/PE4YjpOSiITfY3+emXdpJKRbg155fp4XfYR+B69lHOvRzn5heiRotoFR4oi1docJm7EIwhw7faEMdyLYdcjoeSEbCTf3/bM59CArxnOUS4daGdHn/IS6F1SufKZUvlkreHKrNZ8SFIPvaOs6HYnSEdOn6PyaS4nFeVIeb4pNXEq4bAYa1HKwIRqfDHN81VhsGzyAlC+i79fa1Voj8RUsnaWyzEjxhnruuwMPxl5OaSEqEGf4WCr2cj2qqxp6FCGjY5At4A6uMMyE1sewo3n34ujj3J7AZ+EbY5KIKye2CcRVJ/vFyhHxJZqrZTO4CjBFafIS4P2W7RP790auPSf/7UOyYuDI5Xea+2j556l3x+0zyDgbohTsI94NU9bK7K1GHxLIbTmPjTfq2waPTikFLKgDwMJcXodVvvSMIaEg6qTNSs6+QW1bg90W4BiDJzttdTljfrGQdKox1E5KqB5SYAOGOeyOnV7rff+3mrJSoJsc94OrN4QvP3e2cBLbyhrgA5u743+s/ktJM3bX3MC4NhgbGrXC+f7Oa8qwj2EGLV7L7UilaxiLblQ1J9y/izqduvhr2t5UyJMud3EUaqkQK9PV8xnamC2zivSEpG6fiRSCSHEv75EsOTcdetcsKxXdeasdQhhwDAcMJ1GTHcHnB5OnHaw3DUw0Pu7VmIrc7KmtJHCfssgTZakvVNaWqJwwCf7XGSshfsEtPI8uu+aOvXW0vLj0nOCbEPaOMC9dos1Yii7KotCgRGSBJOWzv/6DecdD+sd7KtVVuSEKPzOQUiRzoKdWq2kA3oJe+G9AGidF43X7pXCnXDOkUy0d61irkuXlVJQ17pxAlNMiCkh5S87fF80/D54pOAhDXdeGyUVUvebV6zripRWrOsVcV20nWnOsYMlZTO1xjK9ulmtHsDaGbeg8EjftU/TBdWi1gRjgOJoknLMKMGr93zr2Nfpa1RrDapzdCi9YMxkk/QQYL84xHM21oC4rYDliF+rAcCRAXuA8hyszXr/jTshBqO2PLrklW4YpVQY3uxy3+LoCMFIjLjpInyJ9vV9KjZaCKb7eW/YKyrL9LITEaDzLCxlz0jAVZyEVDS/VjLLv9bmjLzkfHztEHKpE+OK5mlvPH2W7/UuwG/kekXJL+y+5+H9CM8Rgk4Sjx41U0SnFHUQ5JmLQ73fU/082y9Id75+831Ofrv2e6Ov11w4Oqxbp4+iWktNlXyGzXsFNAt4R+W+AHkInuYgma1eRP8YJd0kXJNcu2Zgpf391lEZnXBdKVeN9FkpZazXBctlweXxgvPHMy6PF8xPVyyztOeOyJzaFGdHkB5hzNP6jVjjzOfljHW9cuBT4JxHCCOm6YR1vUOKFNU6bzEeR+2VIvfprFVGyZoSUsk3GX4JJKTld0rUG8WsdM0+V5RQ4Blp9cF3xp9REt+i84KswVmMUdtG6/rNSbU8tp0uOU3G6TFnPcS7KEx4pc9ojgk5D4IsfRviIU2I9HzzorbZBSlC5uOzXXhw0nZdpKMToP1EUKs6zH1UH8ZAnU+lN4SWZzb+hASN0hQvp0olfs5iva64zgsu6/qsg+x+fPFUCGPQMj6TjLILK+c8JHLN7Lkuy0IGPy5Y1xkxzkgpapRUOoNGk5uIqWysapxLK8hSvEI6yVMXNAPbavpNI5hQT2ZBDYBkEqw1ql71rdK1zpBICB1CtMlqrai2k5flw0mvKVdVPZOSyLzLUQNMfGLjL0+kBo+g6cAA0WnO+TnELfCTtGuttaJ0Ubczt1U07NEV650aYOnON3jPhBL7rCNfO7S379tY2izfK9EVcwK8tajiVfP3DOLm8FdyYW75VOFFYCPfeXtr1n16KAFdhBv4HuwzY987seIMUGvTQQ0/NX/xW+EVa4g0Zc0GIt23MJVDJq0JKS1IKfHh2bUx/Uanh2614xTU546JPLfavbamHYFLHQWr8GWfv66WUS3viExnKHpL3WfLZ752fTKUXKtlh8/32teOWgEj6pDGNI0KboW6zivm84zr46UZ/6czluWCGBfkFNWYiXPovWfScjP8KdE5uS5XrHxmFmmr7TyGoZFKvR+xzoMiBKWrvOidcmOgztBt987rK5GRFsXKUhJsdEie+heUTN0yay5cVdC691kL6t/AEa44TGQXKCCMaUXOESlRNlq6XYYwAAitnM45NJEs5nAVQU0KitvyJ0S35NYyXqCR+FAa9G69hw+Esvjg1AnJ3RkvaZ/lssDNDotZ9D1ThEbodL8GPjiMh5HSOHcHTKcJ42Ek/YCujFAcCtn/aY0AVtIIKK1fznKe8XSaMcfPZfi/KuJnXfTQKXgx1JWlhIFhLVqEpMcf44IUF8S4dhA/aey3vDRHwNxGMiXSOC9lIsjTOvI4nYeNvrU/ZQKg6EgD2wNeIg3ti2xuJ3hZ02DTvpHM3tBTkxAW0ciNvKhchzVyf+cutSGkKNhnxr9/MDUXuOCQk+NIv4f4hWCZIUJGeiALRH6j09MftsLmJYPvMQ0DpjCoEyDGXzUP9E8o6U8dokod+oQ4Kd+rHUzvOunTKvNeKzUI4o59KXiUgRUlY1JCTn/tlI669dm7DZQtMDNAh5QY+mE4cAOepugnxFQ5tLwPGh05FgYJ07BpAOOCpzrsPloSWFSrZpIeAtJDY+U8c4yLRlIvlti+YahR7Zza7Xp7nfsif7aSN6MRnHQ5k0jHBa9rvfA+NX3NuyCNu/d7iUzYrq9LtX1D1CeCVdYYcthzUUdeyptX7lgaF4rYl+WKGOfNuWaNRRgmnkcLKXVopWoFmRGckhNySQRxo+fNsLMvqKeQy5KUCVat3/fssC7xtoqOlCIMDLKT7o+URlvXmSJvF+DXgBBGhBCQhsDP1WukqntGnk0uyClqQLgsF6zLjJhWdXQ8pzWaGJa0uRZZbIG5yXZYQ2kz37M8pY31nuf0hpFjRk4UxTtvYQy3IucWzeNxpMicHbhSClIpiCs1s1suC+anKy6PV3V6af+sSg60nAqzzmE8jjg+nHD3wx3u3t9RWicMXNpM6M28UBopzhFxJXvqSwVM0vWQ1oT5POPxfMHj6Yq7z9zjFw1/7+333pvUUUteX1mNxqFnIPfvIca+5UkrSiEoqY9Scs6wllmLtfDicwqnSo60LytEJRJcCA2itXzgyDXcMpyxqkMvndnECPWOBhHULHJHxOuFLUqpCv8I1EOeZAU8NsZfmNiuAsXmjTb7a8+o/7lEGjVHuo4vtGh8bTSBCPbmXWPtO2PgraUmRgLx7xwMcbrkGvvvp87zJRW/0on5FM3h0r+79wOhLcF5HAZyCnIu8NxHwvHhLNdfUDbkmTcNnVd6TuIAek8H1DgeMU0njOMBIQQtq3opJwdAI12B9vzgMYxBjaCgAJ4rUNTgx4yUWkRBER8dTNQ5c8FypTbUy3JRh1q4NLfdenNqjbDaZQ/vOvPpMxZxktpEazZVN9Y+u/dQG5+gGtMkXTviW98jwFgRCqN5rM6hdvtjW10ETVO9dUgJnTj6tTaia4+CPZ8zMe4tFWc4kh2GCUOY4MMAETeLcX6GathMAQ2tMVpnwzDR2vBNVyKxs5tzUWjXWeprAQwbVOYtIyXSeSdn3/P3WgQpXSd7hDaECQM7stTUpvEYZOSSEOOKZbngen1SdESCvIrK7dZr5zhLa+A9ulkU0icHwREy6jOdH1+R535tyB4DAG9cF5kPGKcBh2nENAQE5zF4pwHBmjLW+4TLuuD6NGP8+ITL4xWXxwsu9oKcM9ZrRVz5XGZ0bzyOuP/xHu//9B4/3t/h4XBAcDQfS0w4LwtSyVjnRponEugWzcwpE9z/6YpfT2fcfcZmfFnAZ9+Vi4d05WuHzkxkkCIwC5UuuSKlgJmRgHVzIEmpk5Rm9OI0YrSJTFKA3UGW0RPZStcbvQDMbJZo4bUSo68Z1jw3vC+9XZ8TlfNQGsrorzM0ZKxh5qujh9Ab/+49aLKFFdsg/R7aavPmFObSSLoU9ajfOvQgEmPWiepI5OvsttSq/71aK3IBvN0a/X3+qSdrEWGrIHbyl3KP3lqYEGBzVgek1Io0EqLig0OOFtkZatOLLmK8YfRICYn5GIQwYByPOBzucTw+4PhwxOHugOEwcK6zGX0ZPeHHMNm0j/iJpDVgmAYMh4EPsQYrU1RvEU1UZ8pxxQMZ0h0syDAtGb7bBHx6p1aeQ89NaUM0Ezrj3zXyEclSqeemVrcJw2GgdcsQcXWWSrU4ihVSVI6pMZcNNmVsxZKBpcipL3dswcbn9B4+NxwjWf3994Q/QWnknCK0ZkDwEa3MjOZmGCYcj+9wvDthOk0kB8wd/OISyTA8PWIYJszzGTlTxO3DiBBGDMMB3g+aeiKCnOSTGXGtRIyslfbrACDdqNwX4wprpMlSQs4OQmyl9MQK5xyWpQVjw3jAsE4YhgOGaWA43NMzY4VBuvaEdV0wz2dcr0+IkaDwYSCHiHgVzJnxLdKXJj669nZnHz0zKm/LKaIYi73exteO5bJQMMEa/S54dlbpiyo86LXOWGpNbg0eJiZXlozzw4JfH0749NsTHn95pPe9LkgpY3666u/fvT8hjAPuf7jDX/34Hn+4f8BpHGENITZPZsaSqNIjLVFJpBvDr05vwbpUjfpxd3r1Hr8uFJRNr+UYdLis84rlSqzWZbnQwmBCksCeOcfubarC/gKHwjo4gEr2GNYJYaKF4Mn7I2eBaqiFwGZFotSYDblNNqK1Dtk5bif6bbrNcu21yx0rfM056JS3nkCt7QsALyCHFEmJraRCNd98qAUmJDrZIHyYWoZ+zc4Z6q9PhXy43StqFarUN42SM2r1G8iY5oC4aKSrX5V93Uf8vaOUuLbYwDTi3m6I0afIv0X2wgfIQqIsBTElLHygDRxBOy7b9AN5+1JrS52rbjv8xSGlv1t4H9Ton07vcHp/wvH+iOk0YjyMGA4jQZ3K+uV745zcukRFpnzwFPWysR8PI6bThOEwaOlYWhPWK0VfghjJvFJ3Qqd5UECiIUqnlZw2MOpbx2bdFxFi6cuXoA5Or+qo/JKUUbnSQu5F4MhSqENfHhJqHRTpAsC10Qlxpqir5JYaM9bC1+21iciNEOj249Z0Rx9NVTTJYsvPzjrTSbRSzn9dr0iZnrE1lBMexyPu7h7w8IcHPPz0gMP9EWEgklotBctlwfnTBeePJ1weL7ieL1jXq36+BEKAMO23KEqPdMitWoo4blfukw54G4b9llEvToD0rEicq68cZFH/empp6/l613nhtEHCus6Yr09Y46z32KeniM3P65tTOsYbdXpaKlUqAzjfbjOMdTAl35ziXK4LYIxycMLgVTiplIJljVhtQqlUNz8YgykMmELAyKXoS0q4Gyf8/UD7ebku+PB3H8gof/qAXBJy/gH3P9yh1orhMODH0x1+PJ1wHAYAwOwJGYil4LqumKcB5vHKz6SSdv8O7TWmakrgc1j/Fw2/5KEBaFlXydQNL66JmaVdtz1r4WCV6axeeJToPemCkXKRnBOstTgMZPAF3iJCyMpeJXmETqCnHDHPZ6S0apRLBD+CRWNcUcodwhhuli0FOqJeBzlrTp83lxiqXAp99hr1i6BKnktL8GFcIvWRNwa1tpyYkJ9qrXCCBviKMniUMug1aTSf08axUmiaHRIpkbt1qCoVO30E8dsuu7KF7GVuelJfYXb6mgS2b+I8MnrtfmsspmA1Xyk5tDWlhgI4R44Ci1WMPiBNUi3RiHA5Z3ImbiR49SkqgjYnjOORoNepRWCSp5vuDhinAX4I2nuhMgl2nVeYT5cNIVY+IwwBh7sDTu+OOI0jzX2pSFPGehgxHAYslwXLgdC19bo2xrDJcNUhjKGLAieUQqTZ+A2GT6DyXn0TaA25Wu3+DobtVMtEwlpq1Y2zcMm21KCQt9h4l1ywXhcypEtk2VOZq6ba6YKjVME4oA4VHp5yYwBXvjR9/Fvvvx+GU3OlFJiFEE/a4yxlnhbUQrXafjxiGCdMxxPu39/h3R/f4f0/+gHv/vAOx/uDiolJTvb86YzLpwuWy8KH9koOUMfnAIAwBMr/HidMp/Y1jIF0+3lbkZQ28XFuGaXrn9JStFxiXeumukQdUUZY1WHx9HymuwOcJwJbyQXXyyNFxV01g/dDW0dVKlYSUo6wWZQLmehXLSor61HaxSElB4PYkfqa7sItY52jzjeAjV6/3HdwFOUH5zB6jykETCFoaggg2dzgPZX75YLr0xW//fr3+MvP/2/EuOLduycc70/446cLOZF8ns4x6t+dtbifRqR8ojOQo/3lsnD1yFa23Af6PKkmeG18heF3naIcGQKFl1gP/3h3gnV3iGvCOi9M7Fs1FxPjyt7dgloynA8aqQsRhqDLrJNL5S0LluWi+S4YAxMMrHHqQMhhUyuRvGJc2RnghxeIkHFrzmf0HoENzbO56Rj8qRSsK7E5l/NMm5jJfJJukLGHxPdDNo6RUjXeTM67jgVuiDXOEGCMaJ+xe19Jv7x19LW7AEe9zmH0AYNzCvP3TH7V3Od7dAakqa7iPAUCwPSHi76/aeWCshaWFHFdI1Khuu2UmzjJFLYVC5UdU+GefEu7VmJgE4LlGMHyfqCUkqMUzjANOD4clZEr5TjWmgZvJjIIaY1YLgUxEXmoZP5+TJTr8wGncYQzzZkstWI5RVxjVIJPWiOWKzF458uM+bxgvS4ouWBIQvyb1AG+ZTQjzspqnTpnLhXWkVPQpxj2eXmV7e50OQA0OVovBD9CbVKUFBYZVonyUcSRoDRZBKV1AHYEihzyXUrpG3T6ASpjboRUDzMY1IHIa2lNsFxSB47W7ud7AIDzjtfEAad3d7j7gQz/Dz884N3xgInh7JQzruuKx3nG+enCqdIm7VtKRZxXzJe55Zu9R5iCavNPpwmHO2KBH4YBwbVrNsZgGgbgen3zvW8Qvlo5oCrK8s8pklyy9RjCqGcQ5fpH+KEJDh3uDggD9RO4Pl0xjBOT9ZyivofDHY7Hd40v4wc413guRAwssK45nd4Z2GwQ16RkUBntfL3tzJcW70JgFz6bcxbeeRynEe+OBxyGEYcQcBgGOGuxpoRrjLiuC+Xlc8HjPOP66YrLpzMef3nEh49/xq+//h0TcVecTu/wh7/7Az7+/BF/ezzgkZ+XIJqyVs7Lgsv5ymJHlCKaz7NeH0D7ipzhLwe7X2H4LXkYLFYhohUlFQzTgMP9ESVnXD5d2fNd2ZtbMF8fcb58wjyflXE8DLJQ2kfnnPTf83zGPJ9RSsa6XHG+fIK1ViMt74dd7tVqOZPtWP7GOIRAmgJSenPLGLyH5wPc14oEUMOOSsxmjUZT0vIagVypAoI9Y2dhS2X5zeYdOy/lW0UPPqCDhzkCEFWvJg8qKROHECZmc2dKgTjymqHe+m2HYElZoWkXtp7tGDwCl9fkyup+hvgQA6MOCjWWgtp5wqVQDn/DURBkxYAUIDukRdMpGyjQqHftrMHoPfI4EPS6Jtjr+kUH62sGRfWOnSw6sPzgMZ0m3P1wj/sf73F8OGI8jgwJEnu/F6lJSJpvpvTYSv0XGN503uJ6oHTB6D2mIShhqDA6Nvp2qAsyFAYiBgoil3NBnNdWfsTR9C1j45R160ic2JyFZyBlgxRp0/rclldJJFIs3WtgCLWx+73uD0mBlFLgstPPlwhPn32nX2+5jExC3p5zcCu/IzgH7ywhXAzf1lpxdZGRlYTxOFKlC3MsBIkIg8fAxvjhMOGnu3u8Px4xBkpdrinhuq64rCtO44jL4YDlPQUqfSls3iFdo/ekwZ6Z8BUzxiFgDEGdb7nOXIqy+28dlJpNyJnO6LjOWNYZtWaO0htxmgivE4aJECrZC5a15Y0QMv2IcTzieHzQzzkd3+F4eofD4Q7TdCLngR1s2Uu1EsICNJJov60ruPKjq5S4dd+nNcIPgc6pJWI+Lxp4BV5jS0zIpSKysQeA67rg03XG04VsYa0VaYl4/PUTzp8umC+zlrqnuGJZrnh8/IBf/vbv8a//X/8aJRcc7g58Da3RT2RkaD7Pqk8hTknfNM95bJQgPze+qklPToUZxVSusM4rwXacu3j67QmPj7+ywaYoY57PWOYzRfnsNcoCGcdjR+AYNlr9Av0T+eMRT08fAUDLpVpLVIIHifjCZVUAnBu38GMpm1zpW4eKSFgLxwtJDJCWcXAEagyXZOWCoLrbUm5BEZN1DmGoem0QWIp5E1rtkIqmC6RkSOVAc2Ed+HbQUTTqsZHxRdnMxVuHQrvcBWxkg++d20jwAqRzMIaA4Nzm8LKGIkSTEh9IFZHhLEkTONs0AIwJsA5N3x949jmZYbCYE1KuSLmrWZacs4iuMNR+yyAnsjH5hX8ynSYcH05k8A8j5TG9bzXqHNECYOh61Y17fSI0KKesQk1CDjPWIK0R03HiOTaKbmjqQhpl8b9lEEraHXRWUlE3VnTUFuFjt4bo+1UVwoTspnO2qUWtqN5ROZw4qtOAYQpd/3g0h4YdA9oDW5hfPktSZsZgUwJpuaFO7ZoyvcbA/9IgISqruufWGHoOtaKcDhgOI4JzOA6DGl7PzoK3TqWqpzDgOFD+1xijaoMyxKkbOK1FqavGFk+lbKBjx9dxXiSqzBvHWa5RUmW3jAbv92XXnG7gc3gYJjXQw3DQGvv+TNI+BlyZAoCc5umEw+EeUv11PD7geLjX4G6cJnKgfWtIU3JBWVvKSTBM+jeVlScWiOuh71vGyqkWLbW1pM7ngkdOGWectTKrDy76Mlsh36WYcX26qv0JYSJBJj7fYpzx6cNH/OU//8vW8CeyWVoqel2xzCtQK1wgbhCly7sUGtzm7Pnc+KomPVqrL3X87IXEJeL89BGPTx9wPn9kRmpSFaoUV2YgUyQuOdJpOjFx7wRRIOtFfmIkUtI8nwGAotuSO49eohmPGBcMwwGHwx0KkwE311+5rfBym+HvhzXmRejYcLkfwY5VI3pjzMZrawSpigAgdQapVqCm5s0JVFqVEV60E2IpWXtObyMraRMrEYoQAm88AMo2IhcyY7+hpKRPkADJy7f7qrB8EEvkEnPGwiiJ8D0G7xA6FKhXBgQfquIcmiLvlzaVAKlklUeWIdDpLcP7lkYQsmqrJaZoYPGLtsl0nnoZGNtK2dKaSOTl0xmXT2ciwl4W4ngwzF8r9LnHOeJwt8CPwh5u60Gi3l4pTOqGl8vCNb6ttNagEf/ePPpOcy9ETxvpZis19VuERfkxXZMa67jDnNsafZEEF4JmKRWZ57mltiiyF4dBW5N2OdhqKos4NUGfW4Z3tOb2VStmHHAaR3KCvde9IQI/fW8K0bgAgJXXfuK1L197joyIg1nTSmTlveWzKirnkw1WzvGKDkYuvcT1TbeuBGrVDjAOIVggjCxOFRAYuW37wqqzlrnvgOSZnXdIay9ERMEfQM9+HI/0fmEgZG0ICFNo6ycXIgx632nz09CUFPMCKAUshNBbyX0rXMzwIkrEXUpFglTF2NJLZ/B2X8j1G2MQxsBpjQeQHPPINmzF+eMTwhgwXwiZLikryh6lDwTzwsLgSSDIteqhfj8RsfLzZ/6XwwHJ3bHxkhaEOZJhvlwfMXNZhsD8SrgzhiVLCbY5Hh9wOj5gmk4YhklZ0/K7ogs9jiRgsfL31/W6eYhGDFDHJt5+tS5eQKsJvnUIm19Y55t8pYG2QRQ1OV89lxBa9XilFl8WRkTTLu9JUZvyJ04Z1E05X90s9n7BKamFDagw6WFuOwEoD81GrFYuGWJjwO/pnevg/7CT6q2sG146A52xxIg1RqwdYzvljME/h/LRvZ9A/n19f+k2Xa1Nzrn/urWky3bRsqynnAvWeYV7srov+rajpVS4SOkb2bznTxc8fnjC44cnXB8vWK8UUVhrOqNelDS7zkweDNKRq5HlJOrvS/3mM5P+pMxHHJ1vcPrkfvqh66uL6oB20Oz3oQzlivA+8N53oiY7jod3yL5F9CW33ui90RdNhFZVAH0/Y7cE1FuG60p4hZTqLCEAA695ABv0KZcKZw1yaSI63lnEDNSU9LVzjLisK+Z1pVSW0QAS0lKt1qApxr4bppwxUeBd25QFyYlopY8GN1p+CKueKlnovKX5Dn6AZ4PVR/lWgw3wGUYkaxHPyqmoARTxq1IGGOMUTaOa/VYmqeiBZQ0Va+Dguv0uYk1NDp4Iz9/C7CGYnUrjItxl0b0fVzK8OaYNf2vTmY/5F677kqBgmAauCLp0wfAIa4nfslyWdmYJ4stGv2/2FNfUSsL5c4cxoJSg699/q+GXD8spd3BzIkGRnCAks1CIjexcRPCDisg0vfIBd3c/4HQSw3+Ac5byknFWhT/Rbs6ZiH+1Vng/dDtjK5QhOe6gJJPQFP5643+zdGdFrqSe1AvLyHU49swD11UX5yhaCh7G8uHOh7zkfZtBL6BUfFU4TPs882JSYlWXt9p7vEDTQ+gN50te6FtGkuthxCflbXSxf9/cwYxikGNOWGKLcOYYKdIRoh5XhHjrNFLRw4SdKqAp+203fWtC1B/StVbVvv8WjkOLWDNqNaxDMcOcuT1mbqkQY6m8K8WsxDPJzT3++ohPf/8bHj88YZ3Fyc0M1bEEdunIs2vC4W5SkqCkKyT6lvr2yNKxkn4TSWi5dlHLu3X0RpyyHtsWqPQadBG4JbGf3WeaAtJVEAKot5toRd7TOotaSeCHUl92o7nfroUrV7j81RDkRn/mb0tvyZDGP4CFsZVSTtYicBQu0XXKGWvOiNoxzaqDKqmtjKxrXfbCdV1xZcPfJKwNvGtObchWr0U+TwKQ3lkCmAQnqpLGwFv3rHrma4ekUxt52GtL6SZLTU2mpHkOkfWCImJ84eoI9MiRGH8iz7KioychICldBrZaEsZwcyPbnHlxKFNK/BWRcrNLtzq94jiINLPMb1ojjCIbRc9qQZVKzijOwct6tgaAIxg+eFLoOz6wAqJXtEOqGnJMiCyCJc2MaqEzbtMoSuwAy2N771GCB7rXmi/A/V8l4FMriFjG5SuFDyHJ9QCAdx4xjO2gZUMtNfXeDzidHnA4PGAcR4Rp4IinUG7PBT0Qc45IOSLGE0TDX3JMMtricSwdOcKrtKPXVr7GmC9OwueGbDQxVOqR1aaF3rPQ5RCSA8k6C8vsbUCUlxLSKpE4R6alLSTp5iSLm5ib9RmM3c+FsY61DSxQHf4h2puKDK4YGjHse8cjlYw1W0UY1GDWgiWKsY9Y+M+YibAkX7VWJNtkR/tDe/BdPXWHusj8i+P10iG3h+G+ZZSctDRODZGIM3UdKv1MoiWlVKQ14vo04/GXT/j0yydcLk/Iida25Lu3cwkljsU1YhhDk+/Nz6P+xFUk6wtRQX+4fsvQ/SNpn/5i2fjK4d23G1WjXqizhjN8XQLLd+Vn7bO4vC+QCptRsmz7uXQ367UDNsqWnUMh13/LqKgdB6WVdUr3QEGwJIqn1wnM3+r/V05nUXor4rKQwb/GSMFELtoPwBrK8dP7FiTnnxH25Bp02Qhhtl/nciZZi1tWvhhxyd97H543zzGioy/GW2SpmWzKwU1OGdVaThN3qcMuRaBnNld3iBSzPLpell1QA1ML6koywJQqXrXioNT8beu+VFRLRFU7t7RRWr1G8XIfxlqY2rgoEqDZ2pwXkaoepwHTccIpPignhngNI6UJS0Wco5756BDLzRlWmsYC+AxyzEFwofX/+Nz4suHnBj1ZtO/5T8rVeBhzgLNU5jTkiJfyKmK8p/GEYRgQpkFzJ8YyZGGJC0Ca0FclQVhDCySlVUkbcrA12IjKSURPniIP8kit+fIkfG6UbsNJ44teY15G3W0xIisxzMXRt4lybVsYUaJHQQK08xKrlkm+eJti2KMfBtZYaG/fYjSU6slObxmZxY9EFjSV7XWQQ5ThsoU17fCT4yZy3j3mjJSJobwm+nviGvuUM0czVHscWZXPWc5n1rohKfV6ClJO2ebi5YP+VsPf1wKXWmBKRYxQsqe5cK1+4c5jc4R1LUKPS8T16YrLb2ecz49Ylguk45kxFiX3sGVbY3GlKppxGuggNZ1cLq+PXhQoar173Vy7C9/G6pZhTOtRoAp9Znuw2Y7USM+EYV9pzVp6h6TtA4GCBba1zkDU+52zinb119I+1yjZT4h9Eq01lOC2e3bGsoHdilTVap9JSFOfDiLeqeAUOwa1VkRe5+dlwdM8Y15Wzdlq3pvrr6PPiD4h5oAplA1ZFhADv33/vhmPOMISkNxSyEvwOyG1QxgRhpEMvbh93dnrLPE1nCPD3UitZPStNSi2CQ/J/VJFiKeUgva4cNqStu/+aGoFYJXvQahXQowRUfhkifZV6fQGbj33DbeIpmCsAPOqiKwobfb9NGpteXwLbhS2W7NCah2PI+Jy1JbcYaAqCD8w+ZObb8V53fBTXjrbhFRLnf1E7ru18/3c+KLhV/WsHVReK9VxCrucIJBxc7PyOoDYoMM4MlvTqR45QFCQsCdpcYwIYUFKU7eBLaSTH012LzLRGM7S0Q+QemG38dLeOvYRaA/1a7SbKL+XmF3aWyZjDKw4Kr12e/eeeqir2ElRBn9JXW0z5/XFE5RDVDZPrRWmVIW4emNxy6CcNrcV5l7PuRY1vnT42I77INBk83x7eDKz4yAISmZ4slYApiqiQPnKAoOkc/85FbI+x79PBaDeLuTSSJK03sjxTEjZAmsXBSaSmXVuUYOXMzkCy5XkSZeFFNlSWhnZsKhMHlTHbWapXun0NcdN/lzvLYs6YVHWuhGymziZlu/5xmffG9y949TWnVFov28hqtA7f36tFdX2ufxdDlcduPYZSvZz7TNlbB1/KZsEfWYRJwObw/etI3gP0zkRpVbUQnC9QTPwDfGj38u1sHObNWhYOc11uc4qvCLiPGr4uyY3PnjEiRzj0XsSgdk5FHTuZHWcJb0weI/Qzc8tg4TXuBkP6/D3Ubfct3TME6IlIAYQyJbq7HO2QIZyneR35cwSRJjQUenkaDbBERl8SdmW1iCJu79SKm4rY36zx4etcylDSrP13jk9J70bdE06izAAtZDDLpUJogLoudRT9kgYAoZpZHlgAxtNC7TiSpVZ6NEVXvddOewwkdz3eBjIAQheFWBfG18B9SdtCiKKXHKTAG96kNQuADpou4eg0o7G6cWKhjO9vBHWxPgBeJaj3z+YDfKhEpIBxsR2LTy+Ra/ddF580Xtqee410WGQGJqvtTaDzxHjntin+S6R33zhHqUXQkpp85peNYuur8n01lpQy/aARL8Z3jjkeVDNqKQ7ykZ2Vw7FfRQkh57AoXlzzYZJUATVlx1a0kOlUqevzwJU0lftVia5sINT9U+oE3Urq1+EpgBaY4bh6n3aSRykPp8uzTRIoCppyZESjyyAnNVh67+kHh6gA0dIbLKGFM5nslvo4G+9nkikwVup3VTFU/RgK5w/RDUAHyoSlTX4FxvYnQ43XiNcmrfJx+v8vYCg7SKm/vWbnG//O5IbLa0d763Gz/PeFWSqdM9HhmVuTw/DrzljjiuWSOksQX5EAyWnxs9QcS9ADb+UkA2HAQu3aB2HoNUBci0x03voeekdaujFjG5n9fdG2Vli8Tt2UiXgaqmkjl/DZwM9G0GnVK2LrkvP+pfr7SUokkBJmj5J8CEIlzjREun3Z4v8eSu/RYJEJ89Donu+9sRNdhpC21oj+06XIowDxhN1ZUStuIZm/GV4lgMejyP1GklU4k38qoScEoACB49qKwByLnxwGKYRYQoq9z2yymcYw7fn+NsNoyOXtbazALbeWRZCGMEuALGjfRhUzclaq3D21gs0qK7CZKuCPimuqjnek7tklJI7J4Elhbk1cCnDxlO7ZVB+r6nS6ZxwHXNiGFuuS2SKraPKg1IrkBpEKhBSUeJL3SxaKYvaQqDb3K0M2qCA99Qr3hTqZyCNS8QJ2xuqrx1SDlW7w1RYxSQnSeQVNdTds9kckB0k3x+W8EDuDirJjxpjtP2vlEbJ/Bc8j/56NKEd+NjkyG4Znh3I4qgBVIrb+xMUICdiFBNcadX4EaHTw/uCUgbEuCiqRW/y/PATgaAwNGEeYGv8COJ2eMkYipGNDBvaeDvDWZj4iQ2UPkOOdowJsN508L/ZPGd5D5qvDoVJQDYZrljlsfTrRTgMe016RQpe6Fap78MoyN5Iv3WQUE5mg888p9L6SADg1FTStMCaMum4zySpLDwMlfXteraL4c+MporRF4RnmAZW5juQONTYO6GFe5CIYpuBB6hpEZ/oQoxd9jf2laNHVCnalDl3u9dVhvHlrHd6Tc47fbVUJmXmqJCq5AwhBuY8sWMoufNGcpN047pErPPC0P7KsuwtxWUt85sggeNtKK8xaJE0N99qhDuuauPnpiS8yo3guEPnOA04vjvieM/S82tiMaItQdVxr5FhGrSG3wenZ1e9UH+bUjOQDYwJ1Bl16FoEs12Vvzv3ZbniL7fltVYhqEao4WY5pbScCliRLVK+BbpoHAaWbBTp39zVLuvr+KCqu0VUsX3PPpcukGmxReGpXBJsds0TZBGbW+FeyWvt88lA05hvEYgBYLQUyBjWdrZbglr7HdogplqSQK1kEEUEKHeSvbU247098F2DmXYGkYz+tpfCW0brBd/qsBX23HnpvXxx//19AyMh4kne3qCxkWXe2muo/a4IlxhjSPI3G60aEWShdF//EHAfQP3BZYj85zba4QYqRshKltXK+Fkz2SYunvtRkPCRYadQmk4VbqpTSoaxVKc77PL7Mp/qVDK8Lt+XaxNdfIpMvo3fUmtlee60cZ6kQRBqha+crghcSge06hVhOzMZWAhLma8pOwcXtmIrci5IZLzpD8Dqb65W+rxStw61RGAihrUnRb1hSA09CffUZ8I7xlAJakyUY1+X+EyqO7M0cy0kyCK5WzJgq/bsgDEaCXpPIlDjcaT3uq7avCmw/kE/t/3c7cc3PftSUEtu3A7OJ/frMeeMEgtrsDRNjlpHJa422yBMfF7vhcvuakS0DjEsiDPlqYc+LVt745+VxEdGP20MP9+0Op63qlYaY+A9oS6HuwPCyKWb3FZ9nVfUtVJ6U1BbAKbrIXG4P+Lu3QnDgZ4j3Uq3j3n/eu3MGTCdJs7P281r58uVlVozSrEAgjoLavQPZPTD4Ddk3NfGlw2/ofKbBm0UFUkQqdxSmwcnvZylVMOjLcCSi+pO94eVese8gERvn+r7E2JcqENfyZs6enq4gcWApHyw4w7wwrPidNwwZBFZNUoGmcuwAHScg6pOghgvAJua55aTpKjeMSQkNZu1VOpshiaKQgQni9r1Q++vrX/vjXOhB2He9NJ+y5AKBDpEpcd7h04YYjGL4AiATUQkJD3P0bsoHlLUl2CNoaiKIynvHAbXMYchwkF9yoVQDvlZ5f8Kw4jQe2/3cevh32DMgSRBIdwWp+VMJDjiVUfdK2Od6/454razOAkWphb6s3tmDR0zys4dpkG5MH1+UfakOOJyXQ1Sr8qav/Xwl7LTvEPmAMAWC7dT9SPn229y7hUNNZLUwQY58BYuuc6pJF+toQVVnRjLkr70YD2MyTDBAIokb9MlciDfLOBjqQdFtPy8APRGTxzg1JE4zx+fMJ8XxGVV+WRRLEwrN++aGapmVEC0DRz3RCFDEHBgzRQpKZOGPCN3gNw7+fLM5Oz5lnI+w/sqsyjOFpGkmnrhl6S4Yo2zptOcD7C2KZBWRuFaCXjkznRk/AFwBdeMZRkQVjJeWp1RtilSSpclFX3b24R2zvqNLXjL8CyF7XkPCkotglnWWSxm0fuz1WrvhuP9Eaf3dzg+HOECkdVFeU/OAlL3pH1OxD5PfSsG3xCGKgRJWsfLtbLhb46GdYY4IdI9sOvi+sV7/JqJ6Nm6rQ1i1khcjHRcFy2lcC5rFF5LwbquTICynOunj47zimXhxj6JDPy6zlQzzU16luXChn8btbtOWY0qAiT63d78prb0jUPqcUVWNjHrXIz8HgLsVb72h9Em97mL0FEbkU4WeGNCWyZRPof7XzJqtRZUFM0t3xrxZy4t1FIxZva3HKLR8r2X4H7DP5dGPqQ335ypmBKMgSIColMvh5Ya9G5Qh0ByJsQ5ULZxNycbXsSNhl8MuANQiuQ4q8pFO+cVlh+mAX4MTT6WjVfi+u64EALlXNBnKGVT0vzneHfC4f6Iw91BvXkh/QihT6JcXdM9ApULEgB7o0RxP1re3rQDvJvPWitrF7guBdhxLMARIRNVpQy41krzk1kBzSVET01RxAjK+4geueSKSdOAzg1jDGAbr0KMvbxWkIPbiZ0k1tOvd0G6pJxORJTE6D9+eMJymbHOUcWVBLFLbOyXy4J5vmBdFzV8dF5RenMYJhzvTxBZYg0AWPtAApieX9HSH5Sa7OWDbx0SNIiaqio58tKi8z9i4Vw7lXdzTxMXaL3GpGdYZJh+Wa5YlutG2dUai7gu8H5BXCcMaYB1Dc2R6+nlyCXS7xFgqjQpHWnwNsNPqVbLUuXU+dIHr021AOYPxYSSLZwFwuBxuDvg+HDE3Q93mI4jdWLltV8r9WkZDqOSdX0QRn5QVGecBtSxW/8i454LYqQyYAh6krsqGSmBVIf98+v+qwR86JDi1ogS+WcSTFhXajywLARH0MQ5LbOz1iNz/2WRgST1J4JRU4oc0c/6XtfrEzMaK8NCBdKUpj1kA1N40SN1hrag78rUow23DIGlpV5X/v5a7Xg/b2V3vZs5lUUtBp/leUvm/B3rJii574X36d+vfeXOcRB1vxvL+biqQGDXnJ/X8b829miESO5aQQpyRrRWS50E2h99k6rtRz/X4mjI12YudtyJb8n1yqYqAFxpDH/J5VtPh8IwBgwMtQkZyHmp7Re1MoPD3aSNmDSn6506wuNxxHQc9b2kLEdSVVLGJ3tS0w7OoBYoItMjAf3h+ZYhamO98VfBIhQUoKk6Clm1NqdLyI1ScrheV60Ost6RE1C66o+Ymj47ROktb9qOEj+Cn6c4znKC9Tyk0hqV3MrvEWc1uCYsVR2w1gp0Rn+5LLg+XalD4sy5+5S1KkfWX2Ll0+v1jPP5E7PRi7LanaPSuRpGnntCAKRErj0DKmVzta0xEQdzhr6k74WIX7110GeVrj4+NXlxXk9pFSSWvoRrVbwgoWSolKuVIvdfecLl8gnLcmFeTICIBZWclLvggoMlZuiz/bv/d4/E9JUCt5L7WuMpo6lukWGnn8v53NKvAzfZOtwdqH+HKm8Cx/sjnYGDx3S3NBRQon7u8Hm4m2Cd030+nSZtw53WpOu7J+7t0V6eoC+eeV82/Jq/EIi6g5kqEelUPEH7IbduezkTqamPVHOOMOsVtVLLXkkRrOuiTkBKtGiMdXCi3rbbxNY4FCMuqIVzHOF2zW7aXNwK91qYWtWLTqUgWIvS5QD7iPd5nr3qBhaBCiKLlC6i78qG2GinSHrX4vD0UJb8qfekh61AQTwPO3nhtw6C51giVsrH6vMcf62tDl+gRrk+geoFHfDSZMVaqtVPmVj6qBTpS2kUOwiSRtCDbwfp9U4ArNnkfPue8LcMqSduYhz0/X1P+OHQiDVhDC3PBnKerDWYTtOmb4ALXp0GF1jIhEU4pAZ/XyWgIj5CtNwYxI5g9A8wqOmNU2ef1h0ffLmS8RdOhayLUmCS8HVapJ/ki+vWbRKHklXX1oi4hNYUhWvyezJVrRXFiNPTEAl5LnIollSUlyDO9C3DO4tSHXyh0rlcDKeutl0mpVumsrrZUbPWIEwU3OSUG8K5HBBj6xxJjcpGDMOEw+mI4/0Bx3cnnLjV88g13i44RlAbpA/DJcJKJmUVPGeZGHur4af1lFJC4vOYGoAFrUIhtVU6t1NcSOeiQ4RjWp9xwpblqp1at6Q8ChLDMDbtCTnTOn7Ry9fqAP5s+reBMU7baN8ymmhabvuVuRXy87QmDCkrAiP5dem2Kr8zMAnv+O5IjbqerliXqLr/3hO8Px5HeE/dLoX7IWiXoA/WW9hi9Fx6jojUr65m+QrDL3nNXZ6cF57kAQVWFmGP3jtalytyTvAuwFjHufyMdaWFQPWYqxJExEmgNEHe1O7LIOJfF9HVosYvF8ofVVlce4/oDcMaoKA16pAcv7WtD32vrlUrZYN7Y+2thRm8NtyhqLE1UBEPMi5UEqMHJac+NLKznR46LGBavqd2998isG9jNwtRLLGCX0lZa+/7IZBbYQepn2uB+4u+5pXP4pSJKwWwdiOGIp/Rf9bm/V+K+gtraH+D4+O8VaEOY4DE612Y9z54eO5/LV9SliPqZYn5HDBGo3djjDoNcqgb0zayiIHQvTTBLClq16i6715XSNhky/XAzRoOorVhGb1I0TwjlUkKQIhbfRdELaXcz38lHkLq3yMX/X1pKdzyulvUpvVmz+rkWE4PqKohR0ySOrtlSMMoYe07loqlNeyaNDIbXj94TJg21yoHdMkVcaGeDaeHI+bzOy3XdIwaHe4OOL474vRw0pKs3inUudKzuFNM5H+LdLjjJmajvxXq5kArJ6xxwRAXQiQGqtqiaH5V2fbC3fvo9yI7Qev22deCmFZFhaW9egiTNq45HE5czUKKrgAYbXyO3lBFkzwT6uJZTeN+Gevwkpjc1wxpRhfXpAgOQOssDJTGiGPQpjkSzVtPaa84R+afWbjDiLtxAkbgOg64jAHrElFSUZKsSHyvS8T8dMWnXx9x/njG5fGC5TyTgiD3uCildDoHfL3sqPRlgt9s+MWTte6FA10jMYk2GsziXKBcDz/wlBOSWzXHmTNBP+fzb1jmM5LqK9PDck6UjCilsIX5G/mrH834EdM0901sboyEiERWOzU5OgQcXyuhAKzl3kHLqmfPKm8WFnXi97QkLARr1EDFJbLHXFmValWSI0W1DlXU0sDtKnlKSmVRn9KRal4ofXzrUEKWHqSiFiYKes3g51JhbLv/Z8a4ktEXIp+UQZIaIkexxgApUaTiHAwjCcZQXh+gpijyfhLtvwR3fYvDI6OHnuX9C3vgysLuvoKUY7mGUNValbwVxtB+j/N76iTIdZdGgN2UejJhTiK9WqgvhEbd8dvudT+oIY401JEovPCare36RKAp5+3891wQywejM5tURd+3opQCWwxKZsfISQQn6Nbu2RZaj8Z2VUUpt1SZ6BDcyHfwzEqnBlyF8/rC9yHH3XtH7G8ptTu19JA0ZfHMCE8LyTdfn6hXe4/WqOF/OGA8TcpG1zni+ellmYX4K8qF1ArYNDSkI0m+dThHVSi5JEViRRuFIv7C5dKpe8ZOnXxIU67cNEiEHGtgEYJXXss4Htnw32E4DLDOERmQz3wp5YuxfZ7Z7Xna60adfLFDtwZ7OdEedMzLkJ731PaWtTMGj8wdNIFW+5/WiAujXdKlEAAOwwDvHBEFfSfVXSgfv1wWPH14xMeff8Onv/+Ey+MFcWl2jyJ/Q4q0rlNIlACgQ96+xtn/KsMvUIPrck1Ai+aU5aza+QO8H1mWUco9VsRIbH/DBxc93K7hTRfFi2dYOH3wXDnKaiRPh2EPiwoBsWuFe2PkA6AjsJFHnRjW9s7B5wxvHXL3/moUS4VzDSKstQLToAY/p4w0JFj2EOX+iMgVeXMxoWS3ho0xQLUoZWWjKup5GXUH8d+6AQpH+wTXEvy0NfilRerdRiu1VRUA0IY+lknYvXKfyKKW2ghke0QBgDZ4EYO+aVTS398LDsetI4yhoVwCJbK2uqRtwhBYKYvY/LUABU1yWbpoVV/Zw2dHQshz/byV1oCnVmwgTmupDBDshEPkrrNRo79/zjc+dr0+SWf44JBWYt+jFLoOHnqduWjL1B6dIXSDoiFJVcjhJCRFSZ2YrpLlpVr9/XsL78BCoPdWztiQqtuJjsJNMSm1M8Ba+FqRnUNixAcAwjjAeasIThgCDsPA7XOtSvbOy/qsTNEPAcdpxGkcVagnsnBQE+zJWJksVhKp42mnQq6skRw/0KpebhlElM68HikVG8KwMbRq1AGq6NmTQTlF2Rtr0fP3flApYGrTfkQYh+YwSyVJkcZlHYu/9p8pa6wFfVun4DbHJ62R58F1DbASOeni2AVPMruSbrLEw1k5NTU7S47e4wXrDyvmuwkudMRUQNu1z09XPH54wsc/f8Cvf/cBn375pEZfSoQlQLAdcghA95SWfpevq2T5Cqifc2rqXe7Y212HPCmvG4cJYSDFIoGqG+lMFgTlrw2ou5+tHtKmt+SEXDKMKZTjd0KsiJvc/etEN254w7nuFG8n+cjoc9fCTBd2ueQBa7UqoalRkZaaFY1QLUf8G9WrDi3oD7i951prJe39QgQahX07dGNv7G7eAHKAMuSVuDZZo3chU33mgN5q61Mpni1FhZEkd2uNUYU/mtuCYgyKAWx9XkYlh+Le+we6HCh2XIg3juEw6Ge2zVpaVCUELN/SYClRSkQa50gTFh+cwt9q0GsF5U0NpHRN2OC6vSTK9yD4Etv0xjNVwu6+ZS5uHXTdng13hCsOOWFTLSHrT8rWitlWGgjbWLQN+tp65Wh0Ov/OMc+hO2v4ZNcIEGgOh6ABhMaI5DVL4jLJ7qZ7148mpE868tXa0n7eO1QWTCG4N2AcAgbvMIVB5XadMUilYAoBy5T0jADAvBeH0fttNRCfG1LdQh33LKr3KFZK55ySj11neO1uP7x1hDCA2qWvGvXHdW4RPdCu3xhYT5Upcs6I0yBIJUlWWA4ISQJ4CCOGcaImQENgw0mpK3HYpLxbtEgkfUlIiIMtBO/TOuzWU6c8eMuIkdbM6gzWecB6pRJN4Vk0lb7OALMzJPueno8lct4SVQ9AKjVqZWR3ibg+XvDbz7/h48+/4enDE65PZ6RMCLD3A+tXdHvEdxLJnXKgzAOh798I9csw4mmIJ77ZvA7WFjjrMQ4ThvGg0FAzZAUGmWv+o3ZSirvmO1uPPsMYagnZiBpROQUGtOjoegpKMYoUGJjO+N9u9HNlWF8IarKwTIv6HecBq6VoFuoT0UaptTaIGo3FnAWSlChFyrWM4TRJVcQDRlIqhu+n3dNexGJjBI3BplXfG0YpWQ/PyFKZ0qVvn9KQ0Rt8+XcfmTtjYIOHLw7JZiRnYVlzXA49Y4wiC32DlA2XYpfKuDW6+dwYD6N60Nlyq07TcrOO+0CIoZPOin2dNpjFHgb/rNKg5auNHng9nCspNiGYAq+weHdDfiQR9a1D4X4hpHZQolyfODDShW2r4gdUK44XQ/heHJKueyXnyft8tcCZ/X3SgdvaoGJ3XpTU5fdZbCXdCPX3KT1pfCOOJkBlcwNr6OdAefXgPQbnELyH57UaU8JaKy7rqkqA0raabwKpkJ5//0hrxUbjQvaYiieBlPkkIBFUsRk/c7NkbwiTEhAljZNygolC2JN9yE6688rOB4Cc7XZ9QEiMA0Kg1unypzHYnP8lCak5KeIpqq36bOQcMEQmBKhajOyFIMFWe228ddA9E/oWZ4r4l+tK7aJDVXEcEuEBYAyRSqtE3HSOq9R5JC2GwPX6kr7JKWGdKa9/ebxSrX/OLIPfETP181rQuA8Y5e8yP4IuvDa+QrmPDIfrNqZhL3TvuYM9MTF2tRY22tRmMxuLEnOLGCARA9c5WqeQ/T5S295g2ZTnVecA57l7WiPAtCoDc3OTnpSzErwAbBwAif6lhAYAimhqQyAps2lGk7mLW1xZhz/nzQOzXCbmfKBa/Bci1rIh7pXNAUj1/hYGBZ8zDl8zco4oaWBjtmpNatqhCw3uf9nJkMNJDoNcCgyrGbpiOVXSNe7Z3W9mxETeq39fmeP+0NsT0G4VcSEmPhnz3oAKvLjXzycSFxn99bpoOZfr1L0qE+5KFhnPVQ8ygTab0ef3d82Q9mjGa2NzQNwY9dAbsdaAJ7ZyYhEdQuM6g8xwey5lQ6TVA9rK/UjeWmrUtwa/h/4tkyL79r6ApfeqzZjXUgnyZcU+yesT2/72HD8AFZ/qI2nd+1yhAgC2NuJvqRVLjJg7Se+F2yfnmOj57dKW/I9t6rL7uSAhUvbp7bYyRrQygG1TsVuzm8MwYV2vTQeEe9x751kyu3bPmFo/i64/0HgOG7EmS3X10oVP5HRLqSjCaamSQkjPUExAUq4syeucil717X7pT+5fcuP51+9p6ZS5zivGw/Ds2WiqzlWthPG+ahVU3yo7zn33wqKGP3Eq1TqDYRogYkF9HwZNDfIZAGs0ut/aYXIOh281/GHwSDErzO88icnQzW9FPUQjP1kLuymxsCxUEph44mDTqp5i36pU3tewGI+UCYoQTeL+y33U5xF0kRHkZJRUAgCeS6duGVK7L2Q+KS2Te6b7o41XaoUXD5f/rVC8ENkilxtKV6fCuUS+RoEoicXaVNu2aYCicsmlY9mL80W9ELC5xlsGiWoMWpYlua41ZfQlfXJduVTAFkZEGkzr0Bw5iuSLdjnsv5dy4aiI/t43RqnsbArUWOpLKY1tSoCIk/Xmw384DCgpAyZunnlJ+VkTDCFg6ZpwFq5u0wQ5FVifYdbGxLWL2Rrn2siAaiC5u6T2un/tPOMI2jC5TGrBbx0SkUt3S2stiikasfQRuZYRdV34CgAk6hRNzYkcXLCbKN9pZM/7iFnsfVtWMIS5me8KAFWpL+R4tfy+1LuXdBvaV2pp4lOM6knSoOlHGFQLgB3WmApiIhXT3EWLl8crLo8XqsUurU1xf7gba7STqKRYVBzqQPoO43FEdQ7WWwzebcjNGwSutnTYLeNwuEOMi4q00TmbNeXQf6YMceiMsbDwEM0Wep047VbPQ2MqUKlmXWTfJaDptUcoVWDgmBumz6dkmFJhTHM2awf3i7NxyyDSulSQZM3zxzVtnbZat91f+TNzTJpe1lRcrVxi2pxULRms5DSMB+peK+d/zs1xFUcZgBJYk0mwtp15ct8uUIrpc+OLhn+YRtSyKHxA+TcpK6KacYE3jCEWvjUW1dWOuRkIemchH1kkpdDPc4pcgreFr6mFaUYpXW6plqbbLwcMRyBSY6r1vexlfotynyp3ddGlNc0jFFKfMdh43aLutabmzermzJKLoc8Qh8pziVcVQmKl/u9AYnGWlhsuO/nGfrGXYhTuknaWt4zr/ATnA4Z1JKh/Zgg7J207Kp8tB40xDgaVjA8bKtc5RqKx/5LhX1OGTQlLjHwwbA+vWlvt9pbrIT/nuSlS/1u14cstIwwe2Vp9TrVW+FKRII5F3ThlAPWQx0h5+76cjTZkyzuKoapFIuHmuEm5YF/up2Vu3O9COSSdA9QiqyYLfevhBwi60In5vOBE9FG5jIa4FDX++npnUAulxUwhfgehGlvokhzXuts3RZ05ABuSISDOFOsCrFGh/1tGLhWeVfAG57A+UwMVBIv+HXPCel0xn2dqxXxecP50xtOHJ5w/PuHyeN006tGIllES76kcVBrDjNOA6e6A07sT7n64g/PMCHfUwErEeQh9a6m1fj3emuKcphOVWK+Lwux7EbH2/onPfcrnC4JD6V8Rvcqb62pNwxoBUKtTOifBceWT94EMvxVVR0EC9inObQXOraP/fSknjByZk0MO5Zp4YxCsV10OmZfMMtetIkqCOVahrKTkV7Jnm9U7NU21UmSeRS8j81dJGaE2SW+9X0Nie4NzwGfW/hcNvwt0o71hIU3uVrKUmURHbFBilztjVEdf8/2oHPknniAHwznTmraCJPIZ3g9a0idqV8asyCUqc1QqCoDmXVolkwSVSLxlCImMSvna4Qp0Ep5FctC0+IswfwsRwWqtNNMJSFUqDVqExKd++1DD3n/wtFBE36C0pkh99E/367gCYFvL/S0bYJ7PGIYJcTkicY5fmoz0UqYy9tFAqZW6zwKsqS2vA5ceuWb4i0Fx3c+TZUZz2VRMWNMgzP4+pWugdGkTqctvOfyptEigVgcEJtKoDnxTWjShedvGFfjgWpMaKVezLdJtkqxs7AXe9lY1wkUMqF+/tVYuN4oa4WoOUKIdNsYi43rLqLUCjEY18S6zW6ZmIx4jv1dtbQJVJaPaglIsPD83csqyIhrF5iaPzJwHcYKg63yrvtnfK0AkR2FJt85325TgW4Z0n1QRKXZihXsinSIBrlKJGct1weXxiqcPT3j89RM+/fIJj78+4vHjIy6X31iq94oY18aRslbPuWEgIZ9pOuF4d4+7H+5grMF0GgEQ5BucV/0QKa2V80d4Bf2euGVMxxOJ7QxEMitdakfOWWIXt33mHPVtcZ7KuC1zsuyuQ14pWQMX4Q+I3n7fnI1Sy05RYekDQVViuUMGKvq0Z9+R71ZSc0/iq5X7DLAzGcYAUw2L69C8hyEgSJ8F7qqpgSF3YNSufqn9XZxZoKXw5HtC8l1ncibn86LpolIqCiOBxoDTcdLVlVNC32r4hzFgfuoOEyP1xA3GoUYOIuJgkVIrp6CHJb3IIzFFc0SKq3aPa6UaDaa11iCEUZn+Ka2YZ2rnm0PsFkuLqNXjQyOchLBtafnW0fpxOzZYlvP6Rkk6PUNXesfnLtXhHeWvBd7NAgcm6iAGhoOtJ2M/1KowU46ppVbQPPkW5Ylspyi4mZbnV/jrtg0wz2dM0wkpLdoSUyQklxiRSt4cLsJ5AJrDJNct87MxYJ0D0/c8z4UV/5wD4J4dYClnVHFEmWeai6i8kSEWqWHpNXDL2DTI4WvzgYyWlNCJaIxIq5Jx9Mx3YbY5GyBjoEbcMWTr+nw2OxgiHNSrhek8da1eSymqod4bQTHE/fduGVRn3wnFCLk3b9NLmq8XdKFWhSkLr3FTsvJVqivI2TIsmjes/mLzM0entdnFxnEC0HQEWLGPOuDFVn56Y6J7ZbKp0Htek+jWtVeaml9co0b9y7x2srfSO75VGZlq9Ayj+bTwfnyG5Mlc2O7Zyr4R0uGGUIuGrr11HO4OWK53WJYLB13rxoDTOUP7Wqq25Pty7krZnui60HWxo9C1WO8Nt9gMkS8Ow4gQJm18BQB17VPLolLanIB/iKg/DFJpY7UCJ+fWfpd4RNSRsZTKiputW950nHAYBi3NJOXHbSpmP1IhZCAuEet1UYN/ebwCgOr9S9MeDfA5rWds03SQLoqfG180/NRm1HXehNWH0OD3RroTAy7wf84CBcWNOt9ehcn7VgUgi1pq0gHp8iV57czwU9brKGjRPrjpRfADtTwcW6vUt47MMLTA/ULs6SdWoDZnO7ipdmV/tkn7at7UOdTwPGqWn5fSDk8TtzlmmWtAhDMcSmkiGti99tYNIA2S1nXhBUlNRtZ5xRwjUl9n3s8HtmI9Aul/jdEHKL1ijFGtdO9c51BU/X2Agt2YM2JOOl9i8DMbAlFJe+sgh5H+3sOb1jlY6f8uIjalAHDNgWPVNhij8LTA/WosfctxS+QPoJUGxgREaE5YDX9Km0OoB4x6NAjoYffbRp/n72Vy+8/o71l+Zhyn/oxRjX5qamKQJCUhpLVMWgGlMAJQ+jOgQfyCjPhnqQWWuea2t9rv/iXlwK8cKzdECaU8k+OutalzAlBj3Ouui7a6HzyO90fk+FNr1yv6IlXOLyJiDhO3Vz0M1OXt3RGnd3c43B/VCd1X1Mj+knLDvhom3Yh2HO+PtNeXu64cu3MwuSxX5j7liJyiOoPOBTp7h1EZ/NKIqNdX2Q/haA2B6vvDMKrYFcDd6ozwAYT31dRK6dlshaNuGX5gPsFeiTLn7TmWC2JeeT97jIcRxlkcxwE/nu5wN00ILAQVM1UuZdY+sQaqtSA6DXOMOC8LHscr7NMVtVasS9QUhzTtofuj9F/gToKbAMI+J4Q/u8evmYQwkFiBiJV4zzKSvAiAVlLWe3/9YrHWIwQgJT4ITO8ltt7Nku9PcUXuOsuVnLSzExFPmrxvdRWQ3BAoJzSIOMRx2ggtvHVIBEr3RQ+8N+QAdPNZ4/hPOSigMpoYWm93ifji4uACdSdTw5IyktmmVjb9EfQ9GsSq11HyhguxF/J561iWC+b5TMZ/XrHMK5YrQU7LGrGkqAZYc2KleeQSjVTUDVwvhxa9vsH58juJn3lwHqUWBLetce4RgFKIOS2lkVl02mPSSoSbc/yjOKMSYXi4VLhTV4ZUMIhhbx3kBJXZkg2NMTCZGcmlUO67VJTyXKxmH8237zeHoyfF9XPblw3eGvFqxGRbJkqMta63rvdAg94BwMDktgeyMdyXvrIDVBUmN8bAVPq+sx1Lf3cftVaY3fXp/VZoa+t1iQz1p2dqgm8Zl3WFz1lr8QFJ5b3cHlsUGY8PR8rHH0Y8/OEBcY6bYKZJLTfCojEUuYUhsMKhVREgyfuHKahCoEaOnHuX6BkgpzuxkVlubMd9uJuwXg+YL3faKbVHZIlLRfwpKPKQtP23911jsKEZdGtEyfR5hRWV37H4Wxi03bVA5wBQOxJgTwQkRE4Mf6vu2RNwv3Z472jPu4bGytlM5EzoNaWUYZYV6xyUB7UcEtZEZc+jl0oIw4qlrXJJuzwWKudMpWCJrW3zclk00MpRdAyaKJb0f2llsC0o/1Ka58uGn7uGpZSxzmvrQOYCepGEPWwDAN55DMNI5X2oqDUoi1/a7PbKZZnzSTlmLCs1gZB6/VKzdu/r9etbBM6MUq4XHccjpsMdptOkuuq3DDFGMbcWoBLF9/CfvA5WhD7o962hel89qPpNWpsgiai2xZVEIOKyag9rhbE6pEE2kyEaNYrpYPXaH/wF1t52+C8LdUo8HJ4o+r+cqK2oEJjWiJgSaufU9HCWEo52BDSZFxUoqQZAi16E0U/lUA5j2PYAEARGjH7MrJLH0fA6c0c45iWkGw9AaaakaFMqHJkWuEykDXnOlO8XOBvIyBthDVk7e6nVnsG+MeA9iY0PGlnvzZk2CovXWjVCEaMpBuaWsRdBMk704VkboFJ8t2+i0n6HnX9bYR1QigVMhalVS5O0+YjttOf72n3NHGzJk/vcvpKglu5rTZQiuDHqm2OE4cP7CHBlT9vvmVn/4tzXWoEhUGOWacDdD3f0PQ7vXkJKNPTDVqirP9usMywb7PSzS6V0Uy6y1wBoyqtFj7ey+qe7A5Z5xfFy4kBr7iLq1go2hEGle0v2JDJlhLMQSJit691SxfAbes5apaMQv7SpDpt+DbUy0Vfr+ztV1trIflJxRTahoVNvHdY7NrK0fgGonof0w1AjK7X6nN7xT1Snn0rG0zJjZCR7TQmRnTFV9cxNz0XI8SUXThPNWt8/n2fEeVUkTCrAxonIfXYnbw00bYTXxhetofUW43FETgXrdcVwINbpMDBxzrSIlBbENjo1MLDOawleY95zw5fCym8SJZXC+tAc2fOhLfkk4RPQjfJns2Swcx7BD0yQucN0PCBMTR/9liHGqLAkpGVj7x11waI8s0S728nuf9bPB9DKuVJqJI7lumC+zM3TYwdAHCKgaWVTT3hyKAT9UOirCvmlcKOi2zQMYpwxz+dt1H9ZdGFe3hHkf8oZuTuYNvC/MQA/432kJASpXhVN572QIIaM/v1lrmMpWDm6SSIvPG8NAG2wG9XbHNeUx9yMk3cItWqku9GTKK1kRyoKxPhKCkbSPCLE0tezS27OWChJEQBMMcThcIakUcVYdjyA3Bl9dUI+09XsS6M3+hBkybZcoqQwcs6w2cJnx4pyLxg4dIgAG+3e+ZEcZeNIGDWW28i+GR1ZCrWC0Z0WJbU2ps97RnztkGi5snM68T1IXb826UHr2GcMRYveOQyeHAXNxXfVLL1zLKMv/5X5kjr9/fv0ypUCrwvEn9jol1pJDfCGe6f20BMOdxOuTycsywWJhdb6FKNwqOg896g1w8Aywc/D7RT96L62BMTebojcu3OtuyUhVo3wJp1gpby79kizgb6PpIVuGc47pNgEtMSRTlymR/dP+zWZlntfr6TJkdaE6+MVn7ounYWFfKT5jwhMCfmvZmq3W3NRxGpVTZBV15v0/BingWWOuz4ftTn96VsNv3iwORWMV8pBjdwzPFxH+DBy16DWxEEeakwrYKxKQFJ5XlVVpnVd2gNkwxXjQhDz9WlT4id5HaCHuan9ouo/DxPG8Yjj8QHH4wOm04QwBPWSbhmagihNTpYMOgnP+O4QAvBs81aObHsFLiKfNWg6xdYBT/LSoj5GGgddsyEYGK5p7T3aPt/VuiWmZwfwW0ZcFyzu0oz/dW7e6HnGdV4wx4glJQRWMes1+/e50bw/2Pj7iefGmEqHaK0wpcDyfCY+4PYHYEyJv7L2x1YBnXltXvWNrH6JTJ23REZLDj5sjYnkkbXSQ6oKpGHMLhpuTX8c9FQ2Rh0LnTvHr9FrgaIClE/m7nldPk+EgUpqh8etrPZ+bVk10K2en6BLUivM1iI5Tsn1B5HI+O4cEHF+NZ2AHQ/FGv28TQlhZ/zpn1X5HD3/hNCyFRW33TsAXJYV1hjNk1su69M0H9oar6ibdr16n936XmKkGn9WE9yvC+3hYIzqswfvAO8BW2CqUSRR8sWldqxwbxWZlD9LKbi74d6HacB0mjBfJhzuDrheSdCnGf+qKVXpyOp9J5bGFVnCxN8q/T1vriaVDVSd5akkFoB0WgTXvVPjskUNf+XzdJNiNq0a4FYNC+csctqn3qp2TS2Z+m44T+idpN/SGjEDiGuEuzolJdYqBFVo7b7szz7613JV6TkR02YfGwPYwKW+h0EJxZqKyEXJv2vw2s3zpfHliJ898zAGNfojC0oslxPm+bxhoW6MUc5IZtX8S0qRISrK4a/8EEWTmUr2Fv0SAw9QORi9f2u32KIRp0b/cHzA6fiA4/GO6145X3ajgM+r88Lev+ea2mTLht2rg6P+yn9SjqvVR1vL6miO+5+751GOqPO1t2x5sv7ntYg4UIPD5DW3jDUusM7jcnnE4fAbrtd3mM93mJ+umJ+uWC4LLvcLljhh9H6jb95fa99it3SHtzoGO8NMvA337CDV8kCu+SfoLHHf8Nyp5q3E7Gbv/NaoT3SxU2yGrzc8pVTAEKTcE/D6dsDSW15aaXrOzQWuz/feawlf64PRkzhbrhuAqtsJKVB+QVM7uRC3geHumw2/79+bnBLnRL6XHACRJEUnJLKX2ZVrNio1zUx8W5vWfjGopqDkhhjSF3awfm37oBIvoKT23KXiZF1XlgLPm33zlnE9zzoPidfn3TR1jv8W1RShH3lOFCiQ3sXMiF4TgolKzgS2lQph4FLOXJAHj1LrNlXIQUTiCpaaS2ssgMRliBZOrvmGex+nAZGj/vFAXKl5PrfSu5wAT4S9EAY1tNA12uWdO2RS52u/Pozh13Vl2WwoFcnMGWucuWNp7M7Gqs4HjNXeLl5EdW4YYRpINjjmzbyT9C4JGwXPLZN90hSbdFbVyqJAfCBdxwaQMpEw7CsPiARfiuH0gaj/iZS79Afwm3bNFFx0jsKyYuYUII6HV+/xy+V83muf7DCxwMQYMLATMM0nXK9PBC1zr+YGy1UgN7KZGn0m8DUCWlPkk5pR74Ma+Lwr/5D3A1o+aRgOOB4fcHd6h+PpHaa7A22gQWCR2w2/ecFoERRnMDC054uU/T1nuct7eGtpPoeCwAtb2PtxjbRIXmqE9MLoF33mpka5ZGLYMnM2pwgYq2mCt46UViyLQfADzudPOB5/w+nxPSuRkfF/erfgYVoxchcyOQQB7nNgt3Xeex+8MBnSWaPlL3Lfa/d3SodWRPauYyYCzZqSSl6SwVuV1Fe43vdWwy+ev9OcnxBQAT+0SDsbnl9TYbSyxGjuzQ7U0MUFIiu5QExlF7xKsWoVALhKRLQCUkYxL0TNXQ6+VDooM0srL2xkvqWiYZyGLlWQkJPTclMhFtmVIuLC8GStZCj3sH4f0dL9UQRnUUjJzJFzAUMlVEb3ODilYrWcGKVbE6WooqSkxyQ1ltKizV1uGeffzurIrNOq0OlhGDbE3ha1A8E55a0AglYxGsVpu/W60FzJeiqNwxEGSkvmXFQBtB/CI0pFBGFabrjmgrSCr4UO/lwK/viZqO+1IZyu+TwTustp3XWdOZ0Q4UuC96K3b5Gz0VQApRl5b9sCWzNISO0lUh8L/3TIgHZwVC5P2kT7zeg3YaBmXEnlL3zDmT9Mg+pkqPonC4HJvhqmQQXXYh+olaI4E/XgqLzf/eZcl/eUs0sqPkTXH135XmvFLK3AA0TWF/zM6T0l5cnKot9i+INzmPnGvHekKsXykcN5wOFwwrLcAwDW9YqSgYpeZKa1lxW4P6dITO6+3WIXLffMz/6w2+bshAU6EplvmHCY7nDoon0SP7F6vbeMvXcvUadcp7cOg3NImaL+l/Ka1hBzubIhdIxC2NhKmnzwWs/c115v7p/JMLLoUSmqyCly4yMqq0nMhSDZ0foNhp/ynMLuv16fcLl8wuXTCeffzjh/uuD0fsbjNGMaAovyNGldYyi/33c17PhMdE+mOQo9eVHgZMljloqO9JexJor2I+f1BepdLotGuuIx3zr8EJRQ09dOA41w1MPs+5SCGDyFbtlxlmi/r9nvq2AkSu/TXBsnsHcM+fUpsdG/tshyvS43s/oPxwkrp58AIDCxqaRMMt5D0JSUwJAJgKtS008Ih4WF9VKdYjYB+DOHrDYUoLtZWFCFBMkRk/EndbSk9c7XJ2pyEiOt/7guFPXn2xyf+TJrJ8b5PJNcdUz44f4OgxdFutpIfkz08xrpdnX1B0FxGAELaSPiQt+jRk5hJIOlcr3ewztSj4yc1xf1P9FJkCGOmqQL8jEB7+7ffO/jaUIpFfN5ZjJ3k1vPuep5I2p6zaAnNviNkFxroby7sbAK/TcytpRx985i0zCQ8j9Oeaao74u+V0k3yNkkhFq6a751HO4m6upYKpeFihNQ2alecLg/UA+LIG1xM+9bS85/rUh8LVTCywTd3mHPhAgkDgaWy6KfI+u7vS+UDKvQfmrIYo/siYIg/vTjq/f4VYbfe2YyJ6pVPNwfsS5RPezj+k4Pp2RWIBvU2ox9LYWj0NwRM4p6bMTGJ/lDVClTabWZloWARLYWIMg/cLcnqfscpxOm6UROCcMhwxgwniacHk43LQKgRevC5Ada5OqsxRCC9pVXY/UZj71IzqfL6fT5PvSRkrUoxWq+sqIqoYVIXAlrXBDjTCmStFLU3/U/iHG98c4rUopY44J1vWKZz7heH3H+7QHHhyPOH59wfnfCdJowhqC5u9FzT4aOsKcRP5/pZWcAvGsQr0KgwWPlzn3C+qdIn+r2l9gg3uVKYinSFjMnivZiWp8dDl87jtMIYwxVVoSiHvySC3JmWWLnUD33A8idkRbHV41gFwXvIGygS+uUZsy1f/0LZX38SyxaEzdyseu8ksLi2hTi3jpO4wjvHGZnAW5tm3OBCxkuZY48fNMlzxWk0QjAO9ofRqDf7YElY4sMoFv30NdW9hR7WLRC1AsTlsuC69NV73tdZyzrFfNyxrouqPU2x285z1iXqDoI18cLkaz+lPHu3Z0a41JJ2td154PIekv0L18uOKR12Ki3yTxIukfSP4GRxMCk1oLWorekvDH+AFTpLWcmIHuLdYm3Gf5pQEmFteO5bIzz9uTs0DnunEewoxLqKPIncTXhZxGni8mxJWvOnxRdrSwETesa086KZiOYt9TX6++6cwItMBT54/FwW7A33R1o7vg9pUcJQMZ3viy4ixnuIHyXLtoX598Y+K6qp+bS1dv3CIGgiFkdWSkLjMwpkPmjt+34LZlawZcctbMnQI7Ll1DOLxr+h8MBtVZc7JZEkFbSpk4xbc4WEnyZ+eAjZSNhngIgZSfrnpW1bVjoqArT1VKQrYXJFtY26M77QUl90+GeSvemEw6HO4RxUAlQPwQc7g44PLwOe3xuaO9tJvaoMl+RXDuRfpLzKKGT8RVHqGs3K+03RfZW5EWlMY92Y7Kis24YIqPSEpTWmEdUq4QXsXL5o7BeBUWB+dYufQK1EelSov7zxwOePt7h/scrLp8u+OS91jkbUAkjrIXoJlUKd7bv3EWyrQRQnD3D6ECrgqD65KIR/8oGb2VtgfW6qh56SY3vcOu4myZ4Z7FEKsUBSEHLuIgaO8Jl58VrFC6eDZPfjM1wzirb3HUH9Mao8SEhYkR97S6MSGZTBFEYZYhras7PZSEEZCVo9Fan5zSO1EveWlz52uRwSqtVXgpBtELiA4yh9tiEyHUVHDvyIk3c85SApD4E+RJFQNeVLdZanzH54xwZDp7ZQX1CjMtN9w4A6xJx/XRRWN5Yi8unK6sBFhzvD5uunL3R106RbPhFyyMOA9drZ+7X0ZUpsvyqlO71bH6AU6UC/bJT2Ou5L2eqBkoxK69pPazAP/mrN9+7HwKsX5XMuecciUKrdyzPy63R9+mPbLKmbkXF1Zgmxy7l4HuHmM6c2gw+p4CJs9F0C/qvnJNWxYSRzvzTu9uCvdPDSZs7CXoYl6hpFSlpFqKu3HPqHDFjDNKa4KNXHopzTvtuyO8IIW+dSe75ytypVr/P9pWzFrJXxCHNhdIFl8cL5vMM6yxyvkeYPo92fNHwvz8eyXMVJm8ho3+4m7DOJ6zzqh6osMjFaDuOUnNOZBRYfpe6NO06zpWMYgtyNpzH4Z+rNCi1mhXPUo3+dMLd3Tscjw84HO4wnUiiV65XFsE43gb79AvaWaPNMQwKtQMGULl8p9aK5Jzq2PdyvrVSLWfiftPCEE0rqbCV3CJ/MZLWOziGWMWZQIUafZHTFIMf44K4zqyQeHt+U4Z4+LVS5L+wjsKyXHB9ojrT6xPVmZ6ngCC1zjL39CbaUlea7OxLq/ueB1I9IX9POSOJ0S+tbn9Zo1YXiBNFkS5H/JmcJH6IN93/3TRhCgFzjLiuK0ouCItH9B7JJpR12yhICE2ZDy+AjHNcVo3y3JrgQ9d5z9qNIAgA1rlvUL+1FsaRcXBMroMxyLx2NmIfQiBjFOjWRi2HYcBQST9BIs0cMyIzlakc0SrJr2aJXPjzPGCygXVt/UJrto0iABsEZFfeJ68Tp0Fb7+Ztbp+0GpLuAdGfIILwbc8+x0yopkT+teL6eCEholqR//Qe43HEgVEhxyktYFt6KKk+guwpghfUb88Jktf2zkO/LxKz3PvubmKEzp/OmJ+u3ELaIkwB6e5GxUrfE4cbl0i65gknK7oVYeA+AtZTyaklw56d8LiEwGi1054YfEkVSEdVDSxL1bOtyR1T2kYCg3ZNSVNsUjroB4/TuyMefnq46f5P709qx+anK8nzrlekRLy08Tji+nQlZr3I47IzKl35jCFukFTZWLdu2lEDXTMe5uaIJv86L5q2oj4IHt54DRSELyOOw/nTGZ9+/g3X61lTMl9CuL9o+H+6v1dDVgVqHUjUh+o8JzL8HLEK/Nxg/NLl60urY+f/7/M0IvNLRMFdDoejSdGDHoYDTqf3uLv7EXd3P+DugUl9ByJeWGdYdfC2Uj4ZylZHg6RtV9oHALl46ujFLTwTO0nCTBdFOtKqLpyXTVvd/i66k3rvbLJGeqWQ50xzydFeXDdfiVsYJ86H3Qr1Ak0zAGjdElvVBcHK16cr5suM4TDgiUv6JMcJ4Jnxh/z7hdEjQxV1c0DmypE+1ykv1wXLedZ6fSnhW+eFdNpZ4GObg3zbuJ9GlAocYoTncq24RLiwQhqG9B6+sP5Vt13ydbVqhOdyQcnEYC65dHm7LTLTp36sI6UuyftaPlAoykibUjZijS+shTHf7PxNLMoU+FmmUhCHFlVtrs8alLzlJDg58DPJ9horMG9tRl0bCbW0llQ/2M4JaI6bGP2oEtKSeyfxppWc0vkJ18snRIajbxm1UvmWpE/EoK5LRMkU3d3/eI/6ngyBGG4h+Mno9fO1zTTq5vsAnYeW/1TouFZe94wUSme/TIHWclnw9PGJ+DYfn3B9mpFTJub3jfltoIPapcmRwtiJWea0poiflRBCQQiOofughruWoilKA7tFeDRAwG7dgyN95mrEFthI6tgYq68hlv+qlV3OBUynCXfv7/H+j+9uuv93P9zDGIO4RDx9eIKxFiklXK+PyDlieCTbN52o3FGaWEEcF2X5i6R3affeVahImldg+sjnlxr93M7+MHiEKWh5uhj969MVj78+4rfffsH1+sRl7QOWL9z7l6H+acLTPOOyrhhyxnEYEY8Esw3TgOP9QYlUG0hIWjlWYgXTAreoRmB9gayl9Cyj1qxNfLbEpiYNap2HV6P/Dg/3zegf748YuVEC9bOmznwlZWJehrezPMXo91r73lotURMvP3I3L2caRCfrWdvP5j61UUmSVRZHd5AaES/p8p2yWSSPSgamecWyOYR4U3JqHveNUY+zDqWKJ04OmbBrYyQi2XyeCWY8jPDB4+xaWkSJjcagGu5n0M+rMciFGh6R1LFtbVpZx1pgvZSpNnmJ1MRiPs9YRJedjUBkxb4Y40Ywyrvb2L1TGOCsQQrkRadSyOm4LFj8ork5zU06Cw+vzxIAqiFiGoEALzthavh6KNw0boQIUG069dVWyib57YVTHZGN/rpeb7pvACT+Yi2VaVqruglLWDb73Jh2rdpMxxSIaJSmKDIdnh6e0k+0AIjs4bZwvzoBXf8CVKp+kSY8UrmRuMY5pYiVI/3z+Tdc5ycuu7rNAFKTFkJTLo9Nve56vij7mmq6M47xhHTMmMYBY/CKCvaonyBZhZ3YPdTfUJBWHiiGv+RKUS+nVyk6XPD04RGffqEugJ9+fcRypRLEYRhwuD9i+ALc++q9m5Ze07ry2lUNcbMhA4sQJnUu+34NpQS8JjuNLjW2T3HROcmIQneuUSAj9iSj1Ew6I8sFMa3a0G0cD7j/4Q4Pf3jAwx9ui/j/9PAA7xyW64Lpl4kkukvGPD9hmc/wfsDh7oDp7krosiPDXFJoSp+poKaChASR5O7nQGWHc9Fa/sTlsS2FSMj2eBwxniblXABATQVxXnH++ITfPvyC3377GfN8RggjDoc7rNfPp7m+TO7zHsdhoJ7UXI42DIHqeYeA48MJlctu+r73G0GZjuUp5WclJ8QkpTddfX+KSvBrHAAmALLIwzBOOB7v8fDwE+7uf8Dd3QPu3t1hOAxUxtFpXFtrEW/szgagY+wygce0TQkQ/J9yZki0tfB01iLlXU4TAEq3CfqDrf/MPQS68YibRrV4u/KVc1Jin0b8wM0Rrw8DUkcMJOMflUiYOrh1nVcMY8DiLM5s+D1zIkiVzFCFQSXZVkVvLJ39kiulz2mtjktltISN/rJ07H2u1ZdSPor2kzqOlDN2cP42wx+cw2EI1C3QWlZFWzEfBrgnul4ptXHOwQfDh0BjKm8cOmM0x0eVHZ773LsGaVuj3qb+DudaJd9KSEODu+MS1QGKkQz+yimfW5/96IlRri1oS8ESE67j3HKUpT7zZURpbX/fQCMz+dqOHSKBFtUzr+wgkVE0WtpHglZU+kRlioycSZ47LpiXMy6XR1yvj5jn8033LUMao8Q1KbeFIkvLiqKZVUZJYe14f0S6O2CdBgxhW3cvnddUUEqklHk+tAKi6zrY+TuKLMWlpbeuj1f89vNv+PjzR3z8+QOenj4gxgXOOhyOD3A3CpYBjFLUxlURdKmUTIFFbrr9Q5yQ85HPmqBpGiG7kW3YVmbpHJutmqd+RklMTo4ayIgj31KPq1YalZKJ0BdG3L27w8Mf3uHhpwf86eEBYGfoLeOn+zsE73G+zvj4l48IE0XZ6zJjjTOs8zge73C8P2A6TSwLvz1jVrBWQy7aSXR7nx15t5sTy+eCrJ8wDZiOI6Wrj6OS3FPMuD7N+PThIz799jM+ffoFy3LBNJG2jpATXxtfFvBh+ErEakIpGLzXmsKTP24kQ9uNUaROZWarGnz5ku+TRxebQ6CRfivpIKYmyTlO0wnH4zvc3/+Ih4efcDq9x3R3wHQaSdSAiS3DYdB2vIIW3DIaW9c8M8IS7Qfv4VPS6NZtDF5r8tCzuJtx30U6rqEFxjQjoMiHbMiuFJI2hrQ3XhU1EU/7Vrh3HI+w1ml1gDgbK0PJArMLqWyYiFRpPRn+oRM4kkNdmhiVarRphzNQ9bM+OhBoNBWS5l3WqJLBcWFnkdWttDlLamgRGdLbUz2D95jCwM/aqBzq02nB+bezRjc5ZiUDeVbT6iE51aW3Rmv4rXPK4pYafskB9kMhcXYSK8Ovm25086oM4HVdNNrP3QF9y70PnRpjqRVLSng6zjiPF1iWCpb12A8yFAYiSvLSEMMgTo/TQ9HCeSAnAB6QRkfaYrnrUCaOR44J63pl4ulvuF4fsa4zOeI3oj3CvyilqHT1slxQSsI8nzVYWdkYP/x4j/Ud9QYZDoN2eBPoV6tNYusauMl/8/PfnwcAlMS3XBZcHi+4/HbG48cnfPzzR/zylz/j028/43z5hFIy7VnnUev7m5XrlBfSOS8iA51yZNIoXf+yXKiTXpgQQkAJHs6ycJWcvVYMPCTHuzHiEu2Tk8HRfp+6zC0NKlyDeT7jfP4N8/WJegJYj+PxHu/+9B7v//QeP/34gJ/u7pFuMPzvjycchhGfrlf88nCiRm8+IBeC+wHgdHqHw8cjPW8uHbR2VElrY0yT93U7dVfu1FmMAVJGZXU/VwEM3J2TmxMNh6FzLjxX8lQs1wWffvmEDx/+jI+//YxPn/5ey69TWvU8em188USUyKtBMw2WCkNQzfE4twO3J2qQobgCmJWwQV5j2hgpLf3rSH/Smc77QE13pjscj/e4v/8R7979EafTewzTiGEKCOOgMqaeD1cffPOmb1RxEkOu0bx5HsUHZxXa7vW1nbVIJaty30vv3XKbLef1UjtJOSiJN8CwG0P6IpyRedP0kpbObaHnt4zj4R6L9VjWqx7uUl4TpVZ6jtQUh/PLQvi6etI3CExqojmzgC2IGXBVxH22df1yr4Vz+iLLO8dO/YwZtkoEYtg1x9xyioYqIrwnAadbhrMGo2/Eo5QJ6n+aZzwdRzhpF1p6ad5BO6wFQ9tLINCNYh+X9vT6DdqeFxJwbSOlzCVghcVE4hqb0zNHJV728qpUXf/2YbmSJfC6rGz47+cZj6yRIeVY+6gFaHXFJrLxN0lupJUsFgvnqJ95LQ6uAtVSmsBaLXzflC1KXbPmwHPGuq5s9B9xvT5hXSmYCOH2PLfzjXwJgCXGqTvo5fKIuC70vSWqiuVyXXF8OOLA4mG6PlKh3K205WW0QEZftaAon2tkahGOuT5dcfl0xuOHJ/z2l4/45Ze/w4cP/xqPn37Fss5dGVzW9XTLiNKFrjf8jCZK9RDNSWLxNIK/vQuqTb//bIn8XzL4stYzo8AbFDM1kqAY/XW5kp7I5RPiOuPgHjBNJzw8/AHv/0iG/08PD/jp7g5//vnnN9//w+GAUis+3t/jv3h/wuFuwjAc4KzHulJn2A8f/kz9YE4TxuNIOh1j6BA9t6kE2KBetUNRMukyWGuRbYYtrWxPm/EcG2E9c8rn6cMTfv317/Dh17/Dx49/weXyCcYYjOOReRCfv8cvGv6Yk5amCbtUojLHykVhHLDOa4M8uUewLI7EkL5E+z2Jy1oH1AohN2lJn6lM4GMp3sMdjscHnE7vcX//I06n92TsnVPIVA7VXjbUWqPOwC1De20zG13+Lvk7AJtUgDFGme2UGrDIpom8NAhsWwpmrVGvX4byAGSToKVKtimRzKSbVr9PiElzLG4Zp7v3BJMbqrQAoM5FzhHLetXoW3Tyw+CRlojVWZyt5ZIwehaey5q8g7LAnbWqdKVKZ6W0nH5KuEY6YNNCBz+4th2gaGiV7wPclYvTMK5tnFtGqc3xG5zDYRhwN014dzzi17sDaUV46RVesGaaI2MJnpeyNFHpC2PQFtfSMVLaaoozve3A1vKAkRn80ihESkA3xMZlVoi/EaFu43eIoiL1oyDS4mkc8XA44OP9AZfThPm8wF0XFRzZOyolF6pwSL3zIV0NKysiVjL03OPAeQdXK4qzmhuttTGm1WCy0Y9zxDKfMV+fMM9nVndjtOuVFrBfM4aJpMmHaVCmdClZm4dJbjnGBfPlJ0133V/uMN8fMR5GahDGqJCos6nGRCe2Y8xW66APnATZWS4Lzh+f8OnXR3z69Tf88su/wsePf9Fov9aKw4EEep2TFNJt+z6lpDKx8ixz10dlXa+8dz2n0zyz+ltDGutb0yl5D10jIm3NJXtyJqYsqapZn2Nv9HNOiOuM8+UT8Tiujy2vf/8j3v+j9/jxH/+AP/z0Dn+4f8DD4YA/33D/UwjwzuHd8Yi79yccHiiy92EAasH1esXHj3+hKjJtBOfVHnom4sYlbvQaZB76/VJSgR8880WaEqOk9vS8CA6lVMyXhPNvT/j157/g7//+v8Avv/4tnp4+IKWIcThoVcWXUj1ftIZLJP1nyVVJXTodWAZhGmAMcP/jPXxwuDwOuPx2ZkPWDDCxDT/iyhu0wdTSca+R/mRDeD/gcLjD4XCPw3SHkev0j8d7VXzyQzvcrdt2BpS2paKN/y2DiGqdOAeaiA/9bMtOtZ33vpfvBdDymKWV++1+LG+0401QCYu8QIiRSfP6rXTKuSasccs4Hh5ApZcE6ZUsXf86/QARjOFoTOqMUyRo/uwXamTEtf2lFuRCKYBcK2yXhsilqgzvZV31a03MZi79fFXV56dyGUrxlBJUJlqUJvf5t68d87piGUc9CKYQcD+NuB4PeHd3xKeHI55+O2M+z6qVLZt3PFBUDGb7Sv29RAYS6Yt6nxC6NBdYiqJETbM7q4MlRK/5PLM+/bXrosZ9GmqFDbc9+yVFTDlgYinmKQQ2/BPeH0+4vm/kyuW6cqkTNKVlWLhJlPhU1hhArVymWitstgT5ewdb6O+FuxZWWzoDKDofIKOfCuIccT1fcL4QmY/un+BOIkVS3veWMUwDDncTDvcHTB9OCGGCATnA1yt9VhRhq+VCKRYWNbt7P5PTcBg1lVNrJS7KShoT0pQFwAbt61nf8pq4RFweL/j082/4+PFngnc//BmfHn/F09MH5Bwxjkc4R8joMBxUy/2W0ackRF9EjK7k1QG0M9gHDuAIdRzTEcEP3HvEN96KBjEtwq+Fym5b6ndBYqNfdkZ/XQltOZ8/4np9RCmFy7l/wA8//CP8+I9/xDuO9t8dDjgMtyJ9dM5PIeDd4Yj793c4PhwxTSc4H5Cuj3h6+oBff/3XGAYi/3lPzpZE6WEMyMes5D3SFGkNvOT8L4GQPM9SzVLpQ/0wCLmWrn3rdcHThyf8/K9+xs8//0v8+uvf4tOnX7CuV25K5BHCRMHyF4KdLxp+KZ/aN0zxwaPYguAcibW8hzLpBaoSpSJjgBACjsd7XTjiOadISnN9bl96M4cwYRwPGIYDL+iJm0IQy3JwJB88nSYM0wCRVw1D4I030KHDcNItQ5i4fTSjkb5pdbeUqyYHIFdumcm/0og6dQt5KWmmNCdA3xuqDJdtK6FqXamKyvXKl6RKJMr3LmxK8t46xunEvRdYzILromnTRoY/my68Mlo7KDZx1D6GAMsdxbIl9Eg4En0uf+Fuf2siZb6Us5KhenKM6mbHBGPA5DpPDXM4YhKex0upk68Zl3XFaV3hrcUYAgbvcRhG3I0T3h2O+PXhiPP9EdfHC66lEKGGWwGXlFGOI0JpAi2K3PA8mQzO80kznwxnKJ8uXQWzRveN3LZX6VuuC9Zl3pCulE1vb0O6lpiQRkJfPO/x4zDgbpzwcDjgt7sDlocTlRJeF3oead0QuWSUUhTpN7tnUV1zfKstALjVdAIpANoGE+thydoI18cLrpdHXC6PGkyQRKyow5GU9y0jTIFLlg+YjgcMjxTx0XkSkVJVfo1E5jFSDfZyWXB8OLLcredGLYafZ+u/vnlWaDLVADbPfj7PePzwCR8//hkfPtDX09MHXC+fsKxXWOswTRYjo6PDMHFviNvQjrSIalxktjlptEh+n4iTFd5Tgx5/fVIp8cIE4BBGOBdYoS9oWWUj9BU1+spPYqnxzMJtWtpdcud0PDLXoiCEAcfDA969+yPe//Qj3v3hHe7f3+F+OuA4DNr7461jiREjO/unccTp/R3uf7wnPtl0Im7BfManT79gmk4YhoPC/ILmhTEgGHKMainKwRFYX0t+S6EOf8E/j/gZDcyyBn59xK9/+wt++eVf4bePf8Hj4688FxneBW1JP45frugw9TMJ4L/5m7+5aeL+f3n89V//9Ve/9t+2+/893zvw+77/3/O9A7/v+/893zvw+77/1+79s4b/+/g+vo/v4/v4Pr6Pf7vGbUmg7+P7+D6+j+/j+/g+/v9yfDf838f38X18H9/H9/E7Gt8N//fxfXwf38f38X38jsZ3w/99fB/fx/fxfXwfv6Px3fB/H9/H9/F9fB/fx+9ofLbI99+20gbge2nH145/2+4d+H3f/+/53oHf9/3/nu8d+H3f/2v3/kV1j3/6T/+HcM5jGCZM4wnT4Y5FC0hMh0QaSLhHOo05UctzTYq01ys2BtTMxXYSlX0L2p12vTQoebWRjdwMiydI9zP5fOdJxve/9U/+6s0T97/+j//3JPs7BG2WILrJMoxtwhR9u83+2qQ3M1icZaNbXVqbTnkdqeS9oG/NzSxI9jMjdm1KL5cnPD7+ShrW3EiD1Ps8/qP/6H/+5nv/3/yL/wur342qZHZ8d8LduxMeHu5wP03wnQhP4i56qWSsKVMPcW4gI20ni6r75Y2CWckZtWylPeVeAWzmU6ZVhKIAkHTrdcH16Yr1uiJHUpITpax/9j/+7775/v/df/e/CWMs7u5+wI8//mP86Y//Dv74x38HP/3VH/Hwhwcc7iYY7pVNetpNsEV0+EWXv1fpc6a1LhZVR9uJuATnqNsjyz7LyKUg5oTLsuK6rljWiOvjhbu0/YZf/tXf4+d/+TM+fPgLrtcn6iKX003P/p/9s/8FAGAcDzhM9zje3+H07oiRm5L4IWhzmV60p9+r+/4DQBOxar0NWh8KkjJte+ClSuO+g510ggOAkjKW64LL4xXzeUYtFcNEHTr/R/+9f//N9/9/+/MvMNZiuSyYLzMuv11w/nTGcp6xLhE1F1XV7DuvAdB7F7GiJuDVhLn6bowyZ/18SX+HvlUzzVNromOMgR88Hn56wE//pR/xp4cHnMYRBgZPy4y/fPqE/8oN/Qr+g//gf4kQRpxO7+jMO46Y7g94+PEex4cTcsqYn66YLwviSsqZ1EeibPZs/3zkegE8u0c/eO23MkyDatOTxHXrbSE2RQS8zr+d8eHvPuAv//lf8Mvf/oJf/vJn/PbbX/D46VdcWOjnX/yL/+2b7/+f/6/+BT7+/AGPj79ins8kBjYcMAwThkBCTmEMqtMvnWBHVgn1g9feHNKDYS8iJl0a+xbPaY3UhComlEyiUNrqukLPfBc8Tg9HHB9OOL074u6He7z/4zv84Yd3eH86IeWMT9cr/uozzem+aPj1sAUbZNs2Xq+mtv+dvsPUvqsdAJJvNN3vFvBGajrf+l4VMKZSlydg0/igOQKkdmUz/Zu0ujvH4Ea5Aucs/BBUIXA8jLD+hQwJb8q9wpzOU6c8Jt+T/tIi5dgfhnTvPCcwzQEwBpCNb5ssaimeVZsOSHFRSeSc8eIz+ppRS4XlXvDSJep4f8T9/QkPhwmHYYQTpbFaEVOiLoap0+cOXg9zk9t1m/J8XYgCWn1mFLpOZs6CehDIHBluaOGQE2lbZ5bIrHmrjHbLGIYJd6d3ePfuT/jhx7/CD//oJ7z74wNO7+70YBuPIx0AQ+ha6HZOcGf0vXXa8VFVH2Udc18Azw1yvCMnoT/4pX2x49cYY1By6wWRu1aflSWebxnU6IXlnrvnVDO1BDYmwQwBZbe+dK862xy4fcOWUvGS0e+Xaa3b/aLXVSuq7Xt9NOU/6l/u4L1DrSAJ7xv16qW1bE4Zy3nG9emK5Tyr5G6tlCettvXUoAvaBTh2+/yAXqL3hWZchdpMmUL3WbK8TzcHXRCRYtJ+8N46GBiMIcAZi+Bu7E9iLSuk0j6z3mGcyKhJf4jIPQf6XiKou2dYKmBqO6tf6HAq85JTgXVZHXUX3LanCQeL6lBai+k04fT+hPune2pg9HiHeX7CPJzhlsvN+/7yeFHHGYCq4nkf9HnK85NmRvJ3aRVN19w6w+7POXHgpG/DvsEdsF33xkDtWsmkEjqskVQgc0FKpJCactbzBd9i+K11qgPs+IsubuvJ9Q9Xbkwe+nPD0wz8ZhRwX25yjQtal6dKa0imTifDWENdvrwDUka2Fsbmrq/1t+n0+4FaLg7ToB235J6ahv5OelcMvV5ub+xbZyYx+r2z0L83/SmHmtGWltZawHK/cu7sVUtBSaTVHeOCNS4UVd948MuQRhHiiU+nEXcTGf2h641gS0F1Ttvu9mMrWbzV22/fg0YMPSLSJD63xr//vnyIY+QpcNvTtMbPrf0vDmMspumE0917PDz8hHc//IiHn8joUxtOCz94RYE8N4t6FtHJ3kDvCL/0eV2DnlqpSRAqRf/GoNSKAKCwRnqtFWWsyA8HftaVunctJH+a0op84/PfIiymacgzilKKRU5ZD6P++o0xGhGLo/6ZD9I9AHRGDQ0dAPqe7hXG1jZ/3m3PGI4kC1/btzh9JRXEecX1acb18YJlXncoFIBcWyT/UpAjP+zmcR/pv4hk2q2zUDP037W0XvdApQY+ny4YDiPGrjlLcO6mgEea7wBQREuk2EVKt+8uKMZOHE4J2qqzsLUz2rXdJ8Atpo0BuHW8/GzvFClqC+i5bh21rD3eH3H/4z3mMz2j83kiiWBu1XvLmM8XRUy9DwjDiDCM3KyJ0GznLSMRThFls1tvpRQ9s+U+ZDR0t/VskIAI4iQVg2oNjJ77NKcy3ylRx8q0UgOzNSXE3vB/ZnxxZpwafAfHHqU1TnudW7v1qqtG8mbzvT2NsBTAVOrT13tylXsVW0cvKniu790P+r2qsLYxqfMKDUzwG7jprSMwXDgcBjrU97AeG2SF6jddrZ6/X3+ovTT23+//KZ9VK6EfthpktPSIHwKGdMA4LljXBaUkxNi09t86jDVwjiLXMFL/g9M4YvQewbZWxHLdErXKdefSYKr+RpqTBD3EBPEQx+hFYyEoCQCgedywdK3S3KKMoTljuR1Ebx3OeRwOdzid3uPh/ifc/3RPcLe0yXRWIUlNb3XpK2lOos7RZuNvHSL5M9cKsJZ3MYZ2O29mgJwCawk5CJ4chDQOSKeJDoP1geHpBfNy1qY1bx3N2erQFznYU0bh/ZU3CJU4CPxsBInYrb/e8an1OTImTrGMvvcDACAzzM0/1y50HHn3e+jWRjWkr07po/lMDYlyzHqN/O7PIFxZ23RO0Jp0FniGgL5g9MVJ7BEWec/nUXKbF2OA+Tzj8njBMA0IzmPgHil4u93fOCrSf4XOvu6xmH0DqdZmVha3PLPnLXrFyQNqTKjc4dI6ixRTa1Esc8YpJWvNxilwfC4d76mL3tP7O26oNKjNumVIzwvvB4QwYBwP8H5Um+KCdMzzXRM4cZTaGbB3iPt12dZ6CxxlXVnHDSq8g8kGRSw/9yGRec8xUapXviL1OPFfsea/KuK31sEaBxgLY91mwTq3O/x3v69RG9+UIAL0M56UXABDh4gY7ZKhxr/Wz3vtxRR4vhVjDUzOcNmiVqcQya0jcMMFHxwsL6T+ocpC1wOxj+h5KBKyh8V2DU2+BMlvcqnm+cGBWinfFCeMw4QYZ4LOb/D6AepuZz15tYGRjykMCN5v+Bk90iHR6qv3UFtkXzR6gHq/L83Ps8Yu/DPjtt+njpAOPjBHIhdkn2HybVHfOBwwTXc4nd7h9HCP4/2Buu5xe13rWxtOyT/uh8CSfa52P/pIv3cOCk0WGX9xJtEMy8AIy+A94jQgp4xpiTi9v8Pp4xlPv91hXa433buMhkw1bgm8Y5jSPM9B12Y0+vfo0YBXP6f7vJd+3qeAjDFIAFztzpgb1/lLI6eCdaZmSHEhoy/NouTz5X4bMlE5hdU4THr/z07G5/fej5KLGj75vGdwMX+lmPVar4crzkOANbc1J5JhYDXN5wevZ5/+3Ainqahz3adnDF4O+NB9f28HSsqogl5K6pM5QClmWJep+ZtzGgBZ11C34/0B05E6KRL37LbufBJEOusxjBOG4aBOvDgblMdndKLnqnUOy9euR23a4yys9H31AFKGONGlFI7+GzJEMD/zBLgJ0JISnLXPmurtx5cNv6FOV89u7iVYC51n+0KU3sgu2wUM7uwkObNSihp/SjF+JgqmRD5yJiwsG2obnJ1rJBPnPg83fmaEcUAYwmbh7/OTWcktXQ/1veGvO2h6cz9bzxAgR52PU71fcR72gwJDWiy+sKc6jAjrRO0g621wr/SB9p3R76N9ufZcCmKhjoTSaa/Uiooeyt9C/Oog7fu4l+718u1SXzT+/bCWtoxjo+SCh0sFjtuK3jKG8UAtoQ/3ONxNbPQHzts79fj3sOTnEKrXhqAlL6UBaq0Q3zeXqnNsDHMCGOnwgVIy03HC4e6A8TDBX247/Pq9XdE7aQUldzAtrOafjaE1W7rIRId92ej3e+JLBlwMLP28rS1XiARXek6HNZtI7K1DctnrErmtqty7RGUG1RjkkpWrA0EanYUzhHzSXLATZ/pW5RbGMOJpDVKszZmWM7Twc+jSKc+iRj6DIrcEXq4LrvOC4NxnHfDPDr7WMPjm2LoX0M59JKvOCAA0J6DkCusa+LAPBPv3IF93hw4qES7BB4e645gR8kYcpMPdAeN4QAgjcr4N7aJ95ekMDZN2OSQExGGYWrSvUL9/IbX3zM61fbV1hgFbOX9vC0wpypNCLigoLU1iW5pd5jbnjJQS4rJijus/TMRf0S5YopdNf/fO0Fvn9OafTeYLRr//t+GcvynN+IvBfDFi7ibRWCgMYhJQrKWcZ9eO91bIz4UXmLV1u6hzzpqr6X+uc1ir9lZ/KZrRObHt33t4VT4PdutEGKme0Ha8hqos/IgQBiX53TICM20Fzp5C0GhfRi4FqWRi8+eMyKz+mLj9aMrqFCkU+ArSoYc6OwZtc5hnxn9vbHsIkNCXQmQ6726G+kMYqZplOmE8jsRk91Yhx+1h+Dym2xq1rWEjLgtNhcxmAZQsuXUEjE5ZH+n1wxmGIb3TlrLTcYL/7TbDb+02whNEK9vG1FZYm/coLGHLLxlvg/33nnM3npH+Kp7t+d6RBCxHRUApbfatszy/tzlhAFBy5ra0WZ2enMpmTYrBb05qBbzwjiosCnJtCI3lHsPPmO5MEKsM6RJ8bJkPACVC94Z+cy4wEpPWRG2SLwuuwZNzfgPcXfkZuuC5tTqf6cbAmC160++B0jn3dE5VXSOA3Rh/+X1xdDd7N5cOAYRG/5m/rG/XIJ/ngsN4GNnwHzEMo5LzbhnEaaPIvucVKMw/eDL6XLlDwWHH7XlWjWG0+ovvHiVXmGD0/gAik+dcOIAFEr0B/b7hnH930kir57QmrDO17F6c/2JL4q9mPyjJj3vDGzASYLr8VO9hvwB9vA51Ni/9VWirtEVUa+UTk72g2jaSZTbuNnK8HQJ0zm3yVerVdqxMqJeLzWbsP9Y6tKSu3Lc1DIkBApE+i2S91c8uucBUPvAAVFdhK6U6rKOcInjDEgt1gLOz9jx/6wgMZwlTPTgHxwapP4gzs/alnG9NGZE99BQzp0CeR/d7z1icv30Jo76utnl89j6W0CkAKDbDMsnO8Ga86f7DSGU8k0T6ViMw+ft+CHmrP8xklFph2OizrwqgsoFn423oOX4OGZKRa+NQ9NGdtcQ9GI8jhnAb5CsOvjoAfakdH/LW1q3DJekXjhg/F+HvndvnrwGX97X9Ls6TkscqQ+2ZYFAZzlmCYSXPfcNIMfNXQkllk2bY3KsEHnJ9uSADqLaiOkvQLFcBSf7X7VCidt+8B0rh6h0udkJRjpgYw/6cKaXClIIUEzHul4h1jZjGG9EeGDjnGUWiFKdhR0Qql4DXERwAzNWyxHA3hhwiYzU9t7cL/X4vUurrHKzLsNagOnJucsrwg2/OPj93WvMDxsOIcTzC+wHe30buk/cTnoDla7ZceuiU0Oc0GBanm66JK0pkjde6qcrgiYKxQM3bVDA4eKvWorpKqaxChFYUqN0TZ7AkXqcrPfdlXuGCRx3CZ52+ryjns0rss9arsRdYa+vVVFT73CO0r0T7NJtbQ98/zP0QspCOQnCybApjuKSvWPaKixrnWz1/gNi9xgJ9uZ56pt0h1KDQ51FZrdtaTrP7u/xLeFAtV9r+rrkghg9l2GIbP4I9TuepBGX1AeVGcp91BGlTGZrVzyyb+6L7zLVB/aUURSKss1R1UQkCtlbgrNfz3cpo7Q55uh6LWi0ZHCYE7Z8r/b7drCd3q+H3A4ZhxDBSLbFGaoWQHsOkUmstlez554jXNn1TteqhdD8XyN6pjSVNhP7nMgrPMUCGInOKpS/jk7kaxoBhHG+6dwOj5XzGPM/vimOje/2F/bU3EHvUbY906d6SA9NSzjynTJFO52xCUROjRGG9lo4sfCvULwiHwMwCP/fBzMu/B4106Z4NGw+r2g59OXB/Vj5zdLtASAjDElVXQQ5MhamERsQlYp0XLBeqwMGtht8yY30IFOGyodunGfqUZr8mBOEQiF+fxU7PhUoXGQ1Ac2jqzsmUzwPIsSqp0BnSPWOKxh2V1h5GeD/czOoHqLKBNGEawkXkYQ/vvUb3GqwosgFGwJibQxffObkdma9zfPe2pEeNReNG517OROY+0HOPGA9R9QCs+zza89V1/DDPc/wv5dAkIurFKPpofg8DbiO+RhbqIVI9H/rqAa7f7SeR6oszinMogUgvOSaU4F41NF8a+kBzW5RyYZKnNtY0mL9sF4HcF30Pz8p45DM28AAYBZH8V35hvjrDZq1FMaWbJ8OReoBzXvkPbx2Oc1h+CFQz3ldq8JxLbr8f1lrY7gCDzIcs6Bd4Cjyl2znMDe7jAEg+AYbhMWu57LNY7OzTF5GmLw2B+8I4aJ5Tot2cM61V75hx3ASnJGIFgBoTys4QVWe4OoYNojFwHWNZEIBcCUaX1whvIvP8SJoll7I7hJno6OnZ3TR0fTkuH90688AulcHVONgdUvI6o6WM/ffb3t4sf9slTiRHni0f9szlYaKdlBSSU/GcRPgtaF/OxOwvudVl89TwPZe2l11zTIy1G/Em5x2MNUqW1VLjbk6fpUa6ueqh9J44bAxFmalGxLVB/eu0Is4r0ulWtIdJq0LsY4SCUh6VDE/nGPXrwNiWnnV+qwHRpwb6PSl7pjBT3RgDl1taxTCHRdZdKe11cs5KPb0LlOoahgne37b2nXPwYdA8fv/+RCA2z0TiKA0EZGSeQ6MLpS997M84GSRmVjbndEOsS9N56UsoC5e0RjL0mSP/HJOKon1ufDnHL5Fkl9+XA0GhdoGDOQfykrLeHtbdeLadB70//I0xz/JCeOXfYvytJ4jOWoN1do0JesPYRJ2d97nZhAJ/feaQkY0gIkjPPqMInNgOK4u9t9eiq17lbv85Ckezap9z6f/D3p8zW5JtXaLQWJ27771PE5F5835VX716DzNAQMRKxTD+AxjiMzR0DPVpT8H4B4hoaAhIoCCBVAaYgQAYVs331f1uNhFxmt24++oQZrOW7xORkbGzBKib61rYjYxzzj7erjnnmGOOcdO5A1T1y+SGNdvNNDOSELyHK3bztTbSVFtG22XxG+SkNC5ALW2kD30AlUpKmuJ8LNJLra4jfvFz45xD8RkpXUWi37iGYSKFSqn4r85ffl9OXZLXcVHo+lkY6eHawsx/B+so/9GePtpnUw1E912re34LcuGAnzMKB/8+aBD6QAFf2Me3rH6MjyB/i/7Vk2uRc74qCPBZmL9duy//zjfo4dU71RcQin7p8VbQ+1G31/JGGYscZUaa2lXy+yWBN5XacD74TQBQ1I2rwz74STLgnIyrtd93DcpdQ8O1QCd0RLxHv+Y98WkKCbvIOOe4X4Dh26t+Ood2nLVUZGS9Jjk3vsMbZLN79qkdBD5/rph9G/+utW72PPpsVmV0FnXwCvsna+EBZGNgYkKWd/rq9xtDCVYII0K4De3yvo3ryjnJZ9MzAFbX+zI6Ld/fB/kvfS8lPLklMXxd+hHJ1jKQYypNL4Sr/D5B/Vqx85sqfmNav0JmcmttJC3aZC3Dwk5HH7afcd3PfQsTcnGoS5ODz10wGeewdvvgVVFPKkg2Y7mssM6hhtvg7pLy1efLZp/1BvVse/nWbUb79u+bcyptU+ur+1IqzNX1uEYVSkc4Mpb4DsVye8YFhDCglNsCv157PlapOAHoDL9Az9WYTVXXo0LWOzg+ZlcIMjTyHGkCI+qFXaarz9dnDm6z6Qi82OBIY6i36oqHT7fd+2k6YLe7J2Jf8Jv72FcoxRjU6mFz3RyrsVsRqlK4X2sMjHVa6ci1FdUtea5l2e5d0YTCGGpzVfojwdB5gvhFaXK6seorpcC5zyByXeJac9nC6lcIoDyXer2EsCvPCPe86XloUKh0ta9bez1adN1GoL83mL+HzW9ZcSX4NC0ROSaWl7Uw3Nf1wRHxdQraB7YM6ffVusjSkuCLV7LYZh+0121A+yaB5JPu7g/LdqeM+TzTMS+UqFyOFxpx24/A4/03n/u2EOMkPNM1kX5ySkmrf5WeTUkDudwLOveKUohkW6yFqZn3jtp4UqCk1QNMmOYRvjUB/L05O/hUkJNrFTcjZRsxHe9+1zifHzyN6zqr90Bg/ZQyynlLGrzel7/UrnnzM7KPd9LlfeEjRdLn4qZhToHsS+tM90YLdffrz/1vLgd0nKerAvrgvsnkf+1kr4I0fXifTV3B2p+BDgEQtGa2QZ/6rg1aFjhonVeUfFvFv2WXtxehZWAM9VmBgwB8BhKvtaLGClcqbU7l7Sb55mf6Ta5DGbRC7h4WoP1+y+Qz7z2rTd1W9RkD9PAznZlRqVgLoBiDxJmmStBCetZWJXvbORWYvEWD5Nhltj+znr9ed9sSiL6HLoEEEqAsdwudheVNxQeHWm+D/KbpQP3CsBXpoJe1MKGrU3K8YmtbZ+Fcq/zpHlsi+GWa2wUa6U8SgT5w9bP98o44S3r+uRStbkutmuiEsWLcZRU2uXW92XCYyyDXoP+ezXsq7/lnEt5NwO4+u+q/MYLDcLHU8USgu9pD+D23oOPq/T9E+vnWtc4r0kqwKUDwr3hW0LQLCVqN+5E24CsYX/dLGW3kXr/vuCLKx+k03aU9ICNZm6Srux+5FKwpYTkvOD4dYazF8dMRy4VG+sI5YJ3Xm859g8xyYJdnXgi7+n2WnvMcZbqiuz+ZevG1ehib9DP7SQBKXridA6AU27H4cxMEAjbiTIJqUsLJSaXbkuzCDT4FAKiHrxB/URQuloqUcic61pKvN9dQEFdn0Ms2A9B9sNfjj5Eq9phWpLRwYpUo6TCW246E4Frr4L3HMOwQWKzMOYvLfsT+fof9Q4Z7wya8OsevXYRSMkrhgyhyw+lBlxOrtW76E6667oHlF3tT4X4mk0ereuXvBDXJ91xd2M9Ais50PUcOlDklxMVqVvmtS7NReVi7RECgFoUAtc9fVMN8A1uCYB01bhBWsGmbnHVArWaTXMgDJv2bHJNCe/35CxxL/Aqn7P7o5pvO/RrCFX344Jz2nBMAUwqcNcgckAC8UfXjv/Bcc9Z/bxmvSFCmzcskSRK8I8jcmTckoc3xeoPQSY7eOsoH4GqMr411CilJEk9jDPNLtg+pdXRNXC6N6c8JgBPSI19LCu5bHowxZjPe1+v7t5/BhggoEOl0mJBjwvx4d9O5N8RGNtO3bPQvVdPXifL1v30OxfvcZ6kqZildBdT3PyuAqiQqOV75e5aW0Q0rzpHhU4JUSSRmxO5+j93drgnG3O0w7EjrozesKrU28xWeDLhGPEQLQoJ9cA6D95hCIL0M7zE4R600aygAyHNdK47zjA/HI6w1JN5yXrDOK3LKWC8k6HPLMuj0BLqEV4KYtFk2RVq3b5eS27vN3Ko2/rp9FvqNXRFC24iQnkcKe/OrMMiYIQfnSqY9IqZDUx3+5oJHjKdqJZ7Y5yD4ZTkjp4iUo369FzWz1sP7QPLBbtsOAtDM1nJCzhHrMmNZzvRnnbGuF5Lc5laaKOiGMLBhEOkVTNMBOVJyHybWMrjfY/+w/9Vz/OqVyTm1XhofQAgDwjRsNdNLRSqJK+2sAbuXMFT4qLx9YPTCyYNgDFKtqrr2psIwBsZU9G2Cfqk6VKmIa7x5jr83TxBpWGclcFuFWlqlmpETYEoT9EGtmwq25EywYGHGeS9ZXCvEW0PVq2Q6oZNpLFdVsWTe/eZMx0gKVLede5dhSxVv2+YjS8R8jCc0YOBq5HPfmxMlPuSex2OArDwlm630towxRBJ0FrZsq2mVyO0yfzHFoeqbKowc080THbvdHabDhGEamMnrNoTBPqsv1xMnIAQKXLVIAmw96acXqf6MQa5tJLUP8MYA3jp28jMbw55caEYc66pa/vLzhHJUjIcJ+4fdTefeIEauZJ3bIC19z1+DMM/x6893n1UYEem9PPrRrk3y7yxItLMiFzLEkX0lxbTpf9Kzn7XNBUCnQuRYb1liRFNrRRCTrrsdDg8HHN4dcPfugMPjHR72O9xPE6YhwPPoYyoZS0yYY8QcIy7rivlMrn7o9rdtEgUN+rthwH4YsBsG7IZAapmcFADNpXHwHqkUnNcV58MFwxSwnJ22oJbLbXPswuonroLT0dWcLav0bdUwr8W5pPgh4ae6IbdhAmypamJlHPFdRATHezIEExlsF6jIDKweKETJ/p2ujJbJniwcgmstim9ZJWedlEgpcvFbkOKKZb1gXWfEuGhhDFBBTIkytRrGgZz86O87fofae0TFYsa6krz28fiE+XLU4J9zRM5Jz8U5B+8HEhSb7tiErSUm0t65POwxP+x/ld/xmwI/vcQ82+kHJQ1p0M8N+khr6yf3VruQm9JVM73trrF2C21jWylukgWFeLpqnzkGOk1gup57LojxRpbPZzJS7V2F1mMRAQ0AXBFmJW2k1DJ+qaCED1G6rF8e3FosjGUjBmyrVpHH1J546vo6LHdprNXjFne12069Q08q9aBjStv2Srdhe+dgC/ewu4pU0IKZr1NOJL0JqfZj0r5h4q8D0JdIBDFoI2ojeqohzhWCEKcAbMh4MLfd+92BA/9Oermd8ZOzLOdMLmZ9OwOAwoE50Xy1VvCJxFd84OvmSFoaaMnV6D28cxg5EAzew2tbAIiJpDmXGN8kVnS/2uhRuHGkq1ZCNCzzRUSUpkYmYMp7VqrOWV+3ryQhlcrcugpkEthy3sEBm6QXgH5/MYZMt9DIT72NKSXEVRFHgMddLUH/m4txw4pM7DOGrG/HPYnD7B522N+TJerDfofH/V79K7yjhCsVglprJfLlyqNswty+HlH13iFNA+qhvSuDdyi1oFQK9MYYlLiiVCDlzEnFquOhMn5HCqNk77peboP6h2lsjpMdyQ38e8zaZtdlX7fOvJHGlsS+oACxMeIRPBxY4VBEcbgF4lgmWIxvUFu/n2baC1I08CzQJauUPqa0hPKWJb3yHDOW5Yy4LsglIaWIlatxEkZLjG5wcQgD6zy3GRqxUBIQa7d7lKAmNq16veR/9P0W1g6aUDjnm1ZJpYQjpRXreiEp4dcBx+cTdg977O73wPuHL57jb2D1c7ByHiGMGEd6GMT6Usa0+lEC2gCv2eZW4Q45Kbm5145MKhIivaWuFwLbTRh01b6wmCUAhCGguLK5yDcvqaitaXOtAj95TzfPGn3QM9t2kuznipU96UmIoZFRAitAScZqBx5/5KowGmaQmpZQ8E1Rhyaa36bA5jgZEDYuXcfPyKf+xqXZe6YK/hKj9pzl//u+8zU/Q7gAZDXLx8QwflzkvkgroxAsukRmAxuAGeriDiakGxfIP4Hm632XGDiF//rr0Cej37IOD9TjD4PXHq4kZ+payDbNWrWWbWsmrgl1qTyysxUzAqDPQ+Gq3VmD4D32XPVNIeh1rLWSAxcoGCwp4byumCNt9L1DmvRlP6ei+VuWzPBb6zZEL/pjYG3VBECuyWa8V8YTO5+NFHmjs6yzEdhhQ5IITqoBYtXHulVr7DXc4xqVXOhFqteKMdfXWc1fW9TfJyRB3CmHadAxN2MMIgdgAJhjhFMSLLDGiNOy4GW+EMv+tOD0csJ6WYmpnoU0Rq6SklgshwkvY8B+aoZYggSKTkY/1bGkhGUlJEHEtmqtKDHfXPHv7nbazgiDFDYdCsfjdder1o6sajKNQBuB/BNS8rAxN46DNbRvT+R9AWktcUsgR0I21yXCnuxmKsqHxqmQBCB1Rcnvuf2JkZ4UV8RVnE4jYlwR40wtG1iNQ7Ko2CF0LIQJA7v6jeMO436HcRqoUPDtGV/Dyu92Qc4JzpG9urSFnGWkg4O+JAUGhh0Iqe2yrmQmdXk54/R0wu5uB/wXXz7Hr7P6YeBcwDBQP2HkCohg1Nx66TFhXVeGJ7JmQjIWJH0P15EUQthu3PJAiJhBGx2hXkoPezTSGWWKwzBoP9YPnmUwW2/p5iUPo8xFB7dJMqyzTERp4jkKieaCuCYslxXLZSFCGFqiMuxIaUqg6yBIgOt7Vxz0MxkyJCbXyLWRfhpBcUlvaT/tYL5C9Pi1JVKZa0w4mQVzjDo3Tp/dAj8AOGvgLcGSgQNW6LgaaUfBaV0iTVvULkjOUatj5x38aLRqFWtkCfhhGjjxEih6m1iWVGh0yJibSU77xz27MvrNxIokHhL4gyM4XnkPLF0c1wg3RxhrsF5WJJUdXTc9UqoQ6L45Y6mv6xy8a54IUuXPccV5WXFaFhyXGadloc+WmepSVABFnp1blkyEuI7YeM2rIFQjN/heE3go6bDv9csUSjEZpUgVRLC+BAHZxKMhnksyjRQmD5FO7aRImuZc+WfnkL1TSdd+lvpbV2ZUofdlcFzsxIX6umdzxhOzywFsuCelFKyXFZfjBctpxnyecXw6YT7NhF7krEnQMA0abMf9+Gb+n8ZhW2uPOCJdZWwNtyXkxlTENcGY2wL/4WGPPXMZiItSAUNQt2WkS6SbHZMqhWVvnUX2hHLmmFFje85zTkiMFuTA7H95trpirpaKyImsJLRy/wUh6X1EZC9WsTbTEshbVkqRkIUckZnbJvcq+IEDrtN/k2ed2jdWIfkhTBhGahEJcjhOgxIHSXdhIQLxC8XGdb00dFDeQbYDlj0+xgUprsilteFLSVjXC86vA8ZPrximX0f6vm7S4zyGYaTRpsMe02GCD77BzJsZ7cR9B8qOiLjQsjC9IMOkoxaV52FtsTCm8MmxGIX2UthbnD+rh4CdI4W6nEfkXOCHiGEM9LBIhW63+vLfumwHR4k2s4q1cAUietvWc8vBt4Sj5IK4rFiWixpHhDBitx4Y9iXFKedoFMs6RwzPRUREkhpwrJcV60rXo9cAt7ZxDZAA2H5W/sZRRg4kookgm1VRUyIW8uiMS+RF3E0j9sOAMXiykHW+wZ+5qLZ15fbQMq/kgpaKjqoIKhTGgGk/KfwoCYDcD4H+B+9boMwZ8xhUXveWJf19qUiEzCnIQxhb75X+0AudS0VMCRfvcemeO7oXadMWEuJYRTeSxz+TcgEQsSaqLE/LgtOyaPCPMRGaNMdtm6E2Kc/e8ORbFmkY7LjCbToGfSAX8qn0q0XBUNG8TS8TOrUhK1sL6zKZoBgWRuEESCZ0Nr8vF0VMVA+iFGTr2L0tKYJGPAcPf+P5C5tfzsUYQvCW84L1sijfRmDh6+JFgm9colrmHj8dcXk56/sL0D5weDhg/3DA/mHPhUCrnpvGRSugnLfKOZj2E8JEUyuSNMv9X24kNu7u99jd02c7b4mXc9WmNTZxwgGEgUfxvIMfQzM4uqyc2EeGyldlqhvLYjvjduJG2jk0Tkm+A0L4FXTMs3mQFE7TYUIYB56santij0B+y6LWZhvjts4rq965gGk6wHuvCYYgffTNhnk2bJh1mDAdRt1LaAqEnvG0JsznGZfjhQoM55DWO8CS34okgCr6BuJIkU7DjHk+IaVFTXqAM+yRkeivCHd9NfATmW9iuGJU6KcUaJ8TYGg1B+57FKS0UmbC2RMArsx3EKvfa8KefE6OGTHOWFc6ubjOSJpEZIJZGP7wfkDJCaVSFh3igLQOKKXCBY9pP23goFtWM2Vp4zp0sbejV9bSDQd4DCZmrJeFe8AF63rBspxpzMwHqliMwXSgYxStaViDyIRc2WzOrxecjycsy1mTIMkuQ5iUwVprQWHtf9kYb6342yZSsCLCCsLDmbhMFwj6YIyhIH2YkO4S0iFjXwYcxhFTGOCdQ64Fw9o4DTk3oRSZVHCS1MloEyuIiVmQkn9YXMg7h8E7TGHAwGjJmjN7kt8O+4olcxgaMgV0PX5Plb7nnuzoA50T911zLSj8AgoBzlpLL2nZzvo6Y5U8aYxBqQVrqlgTsKSE07Lg9XLBaVmwrFGDTlrJlev6vona161rHCnJH3cj/Bg2G/+G9Gk6rQYmgvVjbYJaFSa7KoJVOk6LIhXN2a9yOyvLxAe3Tail2PqqAFVo1hqU4Bpz3lqE8fZ3XipHQTxyKphPM1WknIzPp1lh4Z7PIMFaeDhxjji9nPD08We8vPyC8/kV63qBMRa73T3evfszHh6+x93jHUntAk2D35hNAHOBVPVgGmla7nNcovJjcm7z8d+6psPEqBprFPisHI+0ciVfiiY2CkuzgU2tFWmMHeJmUdeCZbmglIwYV5RCGvzjNMC5nZKSCxcay2nG5TirLbK0//wQ4KNnwRtp8RCyI3wrKRx+T7uHuBj0rHofEAIXv3fEmg+D37T05F6rlsY0YNiN+v2E6LDDJ1fj62XF8fmI8CnoXhCXleLkSJNEmvDy76ql0n6Y6E9KQjCknr8xFvbp6yj3b7Ll9X7AMI3U23JNWck5Swl/90uoB5cQbZuDTJkCnIMXhQ4O2kErKiPQ3po4461IiZCDzzEc3xy4bhaUBLhAVbNkl9d+0r91XVc4pRSUtegGJXCTHYKSvOK8ohZS0aLWQ2h9upyREmX8xhjsdncw1mDYDdg/7nF4OMAYYOZM14dZH+JaM6MpizrueR+04kDlq2K6zfNGS15AiDQZxkayPpVWTFeFiD64cBiGKaiUpyxvKSgHa5Fcq8r5wuompWQXvh708tColM45C9QXPLVMBBa3FICDbwYeAJCn7ajpt6xhGphfQGiPwMbyUuVaMBqDMQS1LK61IvfcE+swhnb/jTVwrClhnVUb3WkISuCLKaEy1C+6CaP3KOMI7xzOfsXpMm+q+V5JshTRGLhdwCYEbqUwn0cqm5oaefFaElk2YDqeohB1ZK/w9bIiceB3Xqx+a/ss28YjJRkU5bbeJKc/pVLbs2a9w9CNzUmRcusSLgc4QcXaqnAJfpLA9izw9bIoryethIKez8/48OGf8PHjX3A8fsK6znAu4O7uPe9tEev6DuO4VzTReqdiTCMHY4G4x/2EMAQYCyUNSk+85KpV9y1r2A0UxD0jasW2gBM9awWsWE6zTj70eyEJ6Qjy6eCOFvW1Yl0XpERseEE+x8OEe9C75rzFcoYed0Mswfe9qSLK18kSfTv5JFM0t6q1AkDOEbUWtefd7Q7YPx5weNhr4E4xQUZMhXBK6DC1nHf3O9w93mH/uMfd4wF37++xn4i3kUvB60zVXUkiP079etn3aqlYZxrLXE4zYia+gwg1aWLPsbKWxvD/WrH31cDvw0Czg9zTDEPYvHgi5lCYnCWzlDRzyn0gyEbn2OP8Dvv9Haa7hiLIZy12oRd3Meg1BBQ96NoGpM4UEAKPETI5AsZgYHctYf/eTHArLduS8xTDHsdQ87AbNNDIxpYTIxcsoSlsUGGEOhe6c7EYdyPuv7vHu+8e4J3D6TITpLUTn+kJ+487nJ7PuJzONPbBs57rSg9QCCPPr5IsrKxb2xyykdGFqCi8MQu5amXughCWwjiwCYUw2nOn9EcBzPV61FyZCrwngkvWO4XFwtiscF0gKNEPNPLkrcUYaH7ac59d5t6rtTQCx8Ipt6zpMGlroTcpcdzLFi7DfiQi1i5QdR9zRqmFRrp8xHldcVlXTUh6WHzYDRiHQGgBDJYYEVPCEAKG4jAGmuUe93u8PxxQasVpWfDL6yt+Ma8E785VyW49wUqO9ZbVK8ypxGoH1X9uRDLFhLo22FMSE2lt0ObI71HOSCtxH6iio/d02I2otTIhbsZyWRBnSi7XJWpvn4JH0lEqKQp88AhTQN1VbRvcsoYxoBbygpDII8Gs5oI6VhizgwueULnLQpvzElt77jJjWeidP5+ecT4/43x6wfH1E5Z1hmeEaOTWJyEXjva9nGCdxzjucTg8YH93r4S73f0OwzQwxGx0UiDFzFX4ymYtt3E8pv2kz74LHoXRD4CUTNNuRFq58BiIwCwFoPNWW0NjLoqALjPB/PN8xLrMcKyjfzgekFKG8xbTfoKxlpGFiOWycGIJAIw4RCoMe88CIYb6oSCnxNfjdsSLUGUDsHCO9zS+PkwDjLM68QFQAmy9xegGIvVNAfv7PQ6PB9y9u8PufqfETSFsemuRmJw77kfs1h2st0TIA/T7AWib6PxyxvHTK+zzGQBaq9B0SVDJKOtFW+G/tr76ZpC3MfVQRAbUeQ8xpiHSWtZqtlXZjiYBUGEwMldgh/u797h//4Dd/Z421THwKB9VyHIxS9rDwGIcdrjMR+pnxJXHGArD/kUrX8q8RhizY7i7OWv9nsqn5KomCALjCKwpFUEtFcu8IK0R6xJxfjnj9HzC68dXvH58xfHlGefzC9Z11t4eQGiKkDZEavVxv0fgCo9uLEGpwzTg8HinPaHlNPNDIckEwTz0olAbBOgc/W5YaY1YJdgzjFVSxjKvmI8XnF7OmE8zSsqw3qk8rPUWIQZNek4cIGcbsaSEi0w6LKtW485b1ErkrrvHAx5/eMS0n7Tyl5dhOlDb4H6asOtY7xKHZNwp16bZ/jX5yi+tMBLS1dpbVatUWyuctdiFoAz8h90EayxKLTgvK4CZRrus6UZ0DLdiqD8uExOnZUGpxNonUpnF6AOmQH9GFnVx1iLmROzu3BLL5bIo10JmpIUDccvqxUiux6N6GVOAYOXClV/ziufP0Rnw1jOVr1EyTZWzdcRz8aJMWaiFpEH/smJZFu0Ry/EQQuQUQbyeYriV5OWHgEVIoYZV94bmfSBQt/RbLy9nLBdmVh+l/7pCRJ4SJybDOCEME0otujnnkrGuM3OkEmKcqYJnpFTEWki4ZcJud4eHhz/h8U8PuP/+QXkBcU2YjxdcjrRHiJreN597cApVD4xiUSXfpmqct0oyXhdGdIXgx60eaQFK/zquC47HJ1wurxRMw0hjes5hmEYMO6qk5+NFWynn40n3TEFyvAsY9ztFhiKjAFJ5r5eVf/dtiU+MK3Nu7CaISjIliqDT3Q7377mA3Y3KO5gOE6a7HZEgu+KJxjBXOGOpfXemiQ/hiIWJkEGJs5TMULtRkonXj684fjriOL7Cv3jM5wsMaH9ZV0IqluUM535nj5/IeDslk9w93jUyCdv/VZah9awYFudIWSePV3hPVdswBhze3WF/TxfKdeI30uN13mHgzw/TgHHdYbwcVMmIxBQyUordfydWuCtcBTTlKN0kbhxrUmJSYkGYbGkWm7X/xVhmOS/ac5UNYLlQMkCjZTSmIdV3CBOGcUfEJu4hrvOK87piPwxYUlJmsfTOiTznMe5GpEfK7JeZILfzy4WkiUUrwDeFLZkm+NYVeY5Z5IhrJejpLEnNp+PGLOLycsbl5Yz94wHz8YLd/R7LeU8/c5nhvUdKCednGjmRh94xS1fmeANX2EL+ESKf5YmB0ZOkqaAI0tdPZUv8AoDgPLy9bQNwPLKUszDlG+GL2ihknxtTwmyNIhAAkGvFmjJOy4Ln8wXn1wvi0hArGmkjAlgpFTNmpJWIYIlVyFQprWOL09gozZkvkvjNK6vD0UYfJuKK/J4+JyUPW2ll6x2CQP6MLkgPO3IFKD1Wbct0GhV9PxzAloV9NTIICEueD8gaeB9QSmsHSNAHiIwoErr0vLCy2+2DDXyMnKBJ0sLaDMt5wevHVzz/8ozz6xnr3Ea+Mqu50bQGkcGkDyvneLlQL5+IYoMm7N4Dxux4j3PcGoxa5CzLGc/Pv+CXX/4RD7/8Cd999/d4/+d3GPcUROfTjMvrGetCs+e3LEGNrDGabI7BY2YkTjwgLscLLscLaoW254S4RuNw0pq1yDljWWdcLq84nZ4RwoT9/gXLhXr4cY1wwWG5LDi9EBHy+eMnRUdI8cnSZNm4g5nbKB0JAa06LbHONOUS421TDTKRJkWZ8HNyzgiDx+5uj8c/v8P7v3uPu/d32HMRuxuo3Sc/M8eI18sJ51eq0k883WSs0Xt1fqF9UDgSzluVixZmvrRtRFciTNT+STLuXhJyIQ4cakFF/eq5f32OX8fFCEaTjAYA4uw0KBFzXfoPUdXlgJZ1++CV4CCjLyVlxLW+2bBlHtvwSN4wEGFPJA7lBZMEQPtMfkAIE0IIKvmovboblso1CpEkG0TE1kPnXnfvUkbjNgTf0zkwG9UF7bk7FwhNGYNmrvNpxuvpjCUSzHU5UvKwLlEfhhSTkiVFSjawcMfleNHsciOAcWvgXyKT7ApKpvt6fr3g+ImCvkBxKuGZC5EQXy/c11q0st/NET54pEhVyfn1rIFfNg0ldpWKuEQNBsQbodZNShnxLmNJCVMMmNeIu2lq4imZvrYmqoorV+a3LOdo4y3nogmeWK7K+S5rxOs8Y+TZ+8AV0hwjXi4XHM8XnJ/PuBwvEG0BsjoVMlhBnDNDwwsur2fEDqIVYs81Q1nZz0x8EuiTxppqp2B4Y+APrFTo2ly1kOaMNUrszDGRGpvvEALbtTK4NZMnmtwgaVX6vpQy4hw7PkDZJFfjRAHRjwEjK+n1hDV6TgJN84jK28DjnuqoeNPpq+hWzCuWrnddimtB/+dnvH56QYyL8mzGYQdjDzS2zAlP5f4t0JIo5wJKSV27csRud6ekZyccKbydzsmMchoYLMsZr09ee+3LZaH2wjIryvStS1CTnmzqjMU0BExDwBKoz7/OK05PJzUJCpeFYH5HomFCNlQeUJx5Fp6u17rMPJrGtrTSnk2ZY0iboTeGFFNpz3dkPqY6L/Q7ss1aRKa0YJ5PN52/iFdd98nD4Em46fsHfPf33+Hu8U6fsZwyjumCFyY+p6Xt4fNpVrSCPp+RviViPlLVX2vd6JPIaDoAnQyRfn/kxCZxjDWwcJYQ9eIC8m+wpPxq4E+ZLqL0y2UJ+SSMg85jhyEgjlHV2XrzmMIyjeOunRDN+1dWbkss27q+MZ9p5LYKXz1KCszmz5rp1FIAYxDCQIxkmYnl+etwoy+5SO5eOyaJbGiOSRmlQgIz1gJjwLAryow1ziIuk2b91jpWQOTAH4m9f3k5I+9GFf4Rze3lPGO5rBv7RiG7AATPhSE0xb5upCrdyO6NS4QPDjlRa0csP1vA3o6qyf8L+WmdF7hTIwVKv5BG92IbmfJtpls+I8eE7B2ijfzfGc7R9YhzxLInsuk4BFxixC40Rv2SEiLDfGJjixv6/M7bpr64Ru1ZW0/TFAtD6ecxbKprOv+EdY686ZF+uvMOdrI6Hiqzx2khgw5Sp6MKWgSrSoc06OezpoMEXvXm5iUCQa0/+u1LnM/kM1xg/Q1GkjInGBK0VZaVg/9GgY3nzI21rTfKwSw7A5lAkf1FhJdUM2HwiGNAUPvRdr5hCkqqUnSoI4OaG5M+er+JRW0vqwr3OE5KZcxMAr4xTgmRsufQH5K5tZ6SSCG2EXl5hbVe4fvD/lFl0Ydh0nad3FOZapJ3TUjXwzRQ65UDaGRZ2VuXtGwy/wGaQueaEo6vZzz99IyPf/mA519edKrEhSZ05IPX6vv8csbl8opluegMeikFK/9dUFFj2BmPp5um3Z0q5jnn4V1QCVxCkVlboxMso2mXxETCW02KRHZX4k6XkPJ+u5wX1bEBmrpk5LZwiklVJkW9VUZD5fvTyvyvJW7aXcMYcHo5bybI5JkTdKntt7m1S/l4kYDylRHurwf+tJCBwKVVbzLHLkiAmGmQO5hs4kYZu7VWGNanV2Wu3OQ3U6ILFpeVCDzMymw3Yjvy59iApg/A8jvl4dN5b34Rb/UlB7YWmKpMKBuyaTObAjGK+U5lgw9xCYts+iFViw9N/CMnmsleLouSWCIHyLhEFQGSmVZi05hNUiQbNF2LBvffumSEapjIIV6WtHUCoxXyvVIRO9Z1l0038by5jcQBWZjd3Y9AZmM0K5bRS2LtMrGoVmRr9frnnBHGgDQkxJQRfHsmE+u7GxaSKbXeFPiNtVxNrEosIwVkes5ydDAuMjJiNDnM/Ez3ZkrkzOa1HTZwNSsvbUoZxiwNKi/mTb0mz11PaqrVAR2yJvoHqmJ34/3feKZX8RmwbVy1OpDVekO59Gc5Ie0JgrUCydMzIu2zTQVUiDDqFw8MVan79FkOPrRkwdhmmuIBGNZxF9c8It0yD+fG89dEnyeNaEInqsQ0AC5kJg3+PrCngZA/uRColfa73XKHlGjTNrBIOcI5h/3+EYfDO+z3DxukpB8hpWMSmeImdSvITuIRT0n6iPNzu2TtOlPFWlHhjFXjoeW84OXDC14/vuD16Yjz61mTOT/4NlnCCN1yJhRrnk/MXUgotcDUgloyUiY72ZwyjV97h/3jHg/zA2oFxpepoZhXMt2CQHvv2NK8IEdJ2pp5zrcuMtZxsGa7Z5RcsV4WvJaKy/HSEMlOml2kpcV9T1VotaXJrQCemFovq7ZoPUuuC2eqtRn6712wLGctdPV7OmQIgEr7fml9NRqKgcDMZLL5tNBL1hOeNkiA9OssueXZqpVSL6fa+zhndq+SGd0+OxLYSUiKxvDMpvFKkJKKx1irMrhhCipkID7NtywR6OlHReh4rBJd1DlKhX34gTAGnpnKxhgMeVDHLvkcY2V2lQJiOC0qCpK6Ebd2PNtkp6SiiYbhHrj0hWX2+tZVBXmp9NIF1iwvpWymO0qpcNGpvaYLXtX0AHoxiACUVMaWjJwogFpOAApvakSSGTVwXFtb6jihbbPlC7aBURS+rL+9z22sQU0cBFJhkQxGJiQRZVEZw/PomTN5Rcg4A5GxQOmPiuFKyiLfmdQBkM6bnP30/mtlIZsJoyjeKVPecnJBhMjAolO3k/uA9gzIuWwSD9tQAaChPlKty9+3XBtqP5muIqF+cIa5rEoglYRla39aVKp6e6N4lMz75ujG6MTvWdIzts4SyuQWhvsr7X+PB+yuNA30+nHi4xgNncrEs/3vYAxZxuac4F3Abv+Au4dH7JgQJsRMIck13kQjRkorr9aK9bK2BBlosq43PvfkaBoZom5y5ClmXF6JuJxi3risaquG93R5F8jkpvGuUEWoyukItqC90jbe3++VmBimoGQ9ABrw1dGw8xIQlVHjbic0A21iTJaSMHPGfCLEU/Y3GuVsrcg+2ZfCVEZhrbXwa7NlLpl4XctyRs5EcpS2XhhpvJG4BbynrFHJrRUVpuKLzZzfXfHHSL2S8/EVp6eDSkpKVt+PVaDbEKRApGq/bGwJNyYznBlJeyAlct8qoH665UAmj7D0D/sNxaFVuIFHSWT0ULLDW+Of9O9l05E+qorJsNBCD7sD0BFC560+nCp64Sk7p/llC4jk8UwSn4JOlNQ2OW1XyMxzV/XLUmU5mZ/liYNbV9WX1Oj5SqITl9j6vJn6ttlzxe5aZVgSaa6TvanRxId4EE4Z94U3SBcckbR2g7ZBBPEBoBrwsmlIj1y0AATi9kMAdgP87xjna7rhjc2OSt7ckhAaZumDN7acmg47wOiIZ9lhns/tVf5E5lehdOfgXGVuRfOraK9YC74aUPk5EERBCFhCdLvp3IXEVzsNi7yttnMmPfY+wMgzI5WoomO5aABD4ceW5/4JPaPAFX0jxun5catQYNOeB2CYAySjZM5zNezfGnl96xJUMpqo77Yw1IfdgF1ogb0/1x6R6adqcmqiMyHQ2KIw1O/f3WH/eCBlVE4YBPmSkUrd8zjpz7moEY8URP1SKdlvXMrWn51uMRLEpddca1UfDWn19Il5rabzi3BKlJPj8mxXKyRAmfqQ4D/uRqR7spa11mLllmXtikjZkzQAl8a1kufplqWJCS9JYuMckWzilkTQokQlspnvpVLzndKsnFtaKamHNSiJ7H1pAoRGOcVtb0xF311NKoQDU2liieKaRa0FqK36zyV/daLhN7jzEZP0dHrB/uUeu7uJLjZDWQCU9SpJhlwQ+lKb/1ZIsKsApCesxiU8CmQKoQUCB7fxop6hb3SiQBAClTnkoKKVw43xT4N+V3nLxiaKbj2TWZb1EtAs9+2sQqbyGZKlU8CgF8sYA7+KVj+0xSC/0+wGOA62wqzul1hbOkY5esLUt67KWtp+CGrYkWLGMA3d1AJPHwTfmRC1Cr1WUFVsaMOXTYsSJaPQqCAgIsM57AYd9QSg0BnA95+TCUkqBCmquRBngDcQAJuE7FsWbbxM0uoSWWQRNrJwTMYSUmLtghIsdK659bu3VsV9YkMs+quvOUoMDZ933/Lq76tzvBFOAaMYyuxGnUz41kVVXscR6BMNQCs6Off+uSabYmKpy0YtBEFrLRm3fOaZFJa/oD/0b1fTOf2UAb/fjsdrDSeE2ia4eie/Zel7mclkSa+Ls7CThQsBu7tdQ6U4wGcWr5IiwTqrExcC9U77HUKkZ1Perf3jQRniohth+8DfwbpEiE64vJ7f7EvSk/49S+Sel3lVYnBKiUcrV2WYV84KrLMoAFfifqPyqD4nHPwBKVDayHEfC+Q8yLxIzNCyGp8V0yyuPRd4jgncMspHz6T96kjbl9bnnmlBGQG6Z5LIltxiGDSWVXbyu7R4B0qARLuB1G0pti7LhfkelvVqFuR0jzFOihaUdIX8otleG0PvFCqR8VNcEL/Cb/hNtrzrOlNmwmNJYSLBmpDCpiKSiyQbulxEIG8ukGTGAh3+2g2olatnZxqk3d0UuO0LXq8/k6vC/qJ9y+qrPXkg5L8lYRGjBnkgJREBxLucAqAEYRu3EwA5F5iUYBb67BytVlq9/Ccdj4xa2TfVhXxdXOokYbpVyEM2ahcciwjtUHJRAsr51StxjS51xz6X/zdbhEauqVQoMnEhSaTCtd6rehgAJVJmtrXNpaLyhMSba8QbrgQEfyurP3jAZK3Ercs6KVBSRuJnoRHJePwOBbXQGKTznp0saxOyGfLG5bBV1e13b+RWZYO96iNr0uCsBv5hCuQhMAYM4XblOpELxWfeT2OoYkFmFIQvryT8vYaAZ3RwuaxIjq9NNc3Vj6FbQo3Ypa9vz2gxQEGkOLtJJsTRT7//d77vshy3DmTDld6+bPgiFz3uRlWR7J/RUlpbUJA9ee59cEoCDoPHdL/D4WGvAj3SB+5Jgmr8xeI2AHDZoH1Gk25rPZx1MDf60Qv8XkrBaiiAyATJwtNF62VtBYmz2u4U8yoAMMzX8gOR8ZwLCANNOgUv5jMtudm0TLqg6zwhLFIgyH5Bzn5Dp61Q9d4MYUT9Dez2X1uqCXGtDWGNvs+COoqDbI6ZpdkvWJcLSmdSF8Koo4Iy3SCBP2eq+EWXRvgFPoinDU110DviGdGQorYlHblkxLR+ldj4mxqAOZPBwrKcMZ8OTOoi32apLNW9znvdmCRT6W11+wxeXuC+hylZdikWrlYkMNRkqYIwXBX1so21VO1puNoedtJs9vCpwLrbsmCBuos1ajEqMKcozcHLA+tasOQWA/8AEUOYjSna432vsqSCbDOdqzENOmJNdqnunHcqpUkJgFdIUfYBRUSM4SD4O/r88tByf9oawzK6HmEaWL+Asn/piUoQ1srfGq0i+s+Ve245cNGxQxOqLx3P9bMEtMRMroWMzU0jzdbiBtTD87VWNKFW7bsD1yI3TdGvf76tY0Ii3+thCpjDVsu+DyrdiW6ul8ighnFQYqW0mXpXSD9QwB+DR3AeKefbzj0QUSvjShODkxAicbZE+Fo0SDwOrGfuAyt7FkPEJlso4Fdul/jilZkvLHWgGUVJAaDVlV6mzi+DZ+zlj3XlZm6PiLHI8wwNvC2poPZHRgJ0ykL4S5LISeXfgrIFxInRWfjObVJ4UwLnb94BSYC52ieJbNGGd5tn0TkP58NmKuBbVq3iRZL0PZMWHU0z8Li2sMlZLXGcBlXtA1ry6E9eBXuGYcfXQ8a1O0Mu5qiUq9FoulY0EaM/E5y+B9QbLyzNzqI3w/g7dAw4aex4KtZaKjL5Xa+loFQh9hGZN6UF67ogRvkzb/YKACo8t64S9M/c40+KHnofyMiuJNjClrzWoFaZNshKXhSkXITthEshCcSX1te1+sVHvZDG/HJZ4F/pAMd9agQ37wha3FitZhZnoIdEYHljTPOS7xS96KLTS1QRkbODy9QHcqmgiDses5k3PSURFEkZOTmUwP14J9nh7az+6+pBoOUVUpV7cqhyFjDC6N0am6xLRK3QbJlG4hopq06MDPDLElW1bN2Yb3jpge9HWDdScsMM32uSFR3r79Dq707bWHK/24WAPA44D7RBL2ea9hAN6ThHxFLhTIMBjTGopuhnboJ11/8FAFN5RtxZlBwAT9aktlpkOT+G2gVeozexQqw9FVIdSeFv9B44n7/5/MNEssCWE9swBB033cCS3QZhDBepOnKXtEVhrUVcE+xlbT10Ro5y6nrg2KI98t8yyWKtbRru+xHBeVipJq1VbX/vHPnFL98uZCIBs+/vN+MaTr69g6mtpy/iW4I4BHbKW5fILQ9P0xm5aEUHAFgjIQuWEsxhamOuNAWT3jCk+ypLjjGnApjEkyKOe/63BX5BK3zwGw0gGlNdFa5d51V7vLK02q9V0YvEtrnWWyDhM3teadwQIXTNFGjFoa1WaABOXUGgGiN8T7wLSM7jVnOuHqkQYpmw/GeWJZbnkuS1LavvEbekF2YLg8dymtHcVLeTCtbSuyrKnLuHHfusyGRAgng+9AiGD63FYnkkVK4BXdO32he/dW0Q5VLBPNpWzNWqE2uUILWgTwZqUX1mSkkwYJ4ZDJwPKKWwCd1FpaclIbBx4X/fYxh2MGY7nUUFlkxAEQogBnWlJBQebf/dPX7pyxSeQZ3nk1Y1JWUkHmMrXfUhS+Qct4HLb0afSq5MWGP3O2+BaPhhzshsCiJVdX/YKscp2bWQaDrmr1je3rrKVbWBSpzZvgoKlW0pB7R5fibY1VpRmZEcV/Kb19luGQuSETxHYykotFkmdr9aLwtijJzIeO27yfhWG+PqH/q+tXLbuaseA2/ug3eYBtKUD46saE/M4Acnc8kyFMbBTl3KriqYbWumcDYr5E9StPNrYoa2hTFbidicEsgXoHEGXODZbyYdjcFj9B5DuK3XJ4mOGP/4MSAtcTOqp8+Bjhm2jbInPFme2c8xITH/RKRttWvFwZHmgEUquVW4kQOoCw4pZYRCJJ/Bu03wJ48CVjW7Fep3NMoo96/m7b0TwZ6eW0PCOYMabznnyG2MEYLAzm2uVh1jlfFWovNyQDSG3yHP18zxyFdr9VRggy5lCDeA79WQEW5/7XWenOx+rSaWABRql/9XfYeu7SAtMkG6iHTW2kJyjYX74bmCdcFR4E80Cidqj32RI5wj4RNI8iMJjw8DHJuA3bLiEmkqKnCixqidILgyUuw8jXTKeQy7ZpstngYlF2KoO6eJiIHpAhklSM5b7B/3+OHdI+JDwsfBNwVI76i1UIoGZeJ3NH6U+BXElUjSElRvWT3qIsfbfw3GwPITK/faWg/vCye25CEhyrKiCRCNQWbV2eY1QdC/JvpCEuavGcMWvd5yQZj4+5Kq2IqTYEoRMa2I7N76a+s3lcHUO6CsRH8BjyVIxYmuopYXUtypRGRE7GklmF9nZA2mFdJHJqW7zHCqa2NMm74+aNyvVqMZcK0VVvpt+TaYn05eZocJ6u+PWF4EUYwCOuhKKiZ+GMXYoY0vEuJhjAFiQjTS308wLHhCwYU3NlYrNMbojK4LXtXNZNOhD2k8Cnn5blm9sJK2GhjRqCCkIw2Bv4+JPTFTQLa8OcWi0p3ywkpTuGdc9+S2knl2dY1IQTQBtptYLdCXHWgbqjCN/RAoOQlBJX2/dQU2/jHGII/Ua3POwmcS3ZHkrLcpln/rx4+stbClYrU8rpZr1yLr57S5NcZuYwL3SuUVWSLbOseTAoF+b6jwtmUQwn8whgyDblnybjZjFErWvQRWeK1EqM3BEwk8Qy99Xhc8Bv5MIYTVUpG63q6gH9IvVvTHQq8/HUsBIFV/G2uVZ6DI+bNYTh8wv3X5QFWoMVAVUtmuKvfZE6DwPtD4MOM0IOy9JjowBjZbIi76zo7Z0NRPbydbecSLxLLYlpZH3SS5l0Cn+6dU/FZaMETwvXUtl4WmF3bM0yhVx2+Bxv2RaZ/9/Q6HxwP2D3slAcMYrPPK43uA92Rrezg8sqeCwzCQAuw6R1yOpP73/rBnWe4m0OOHgPPrGXHewtcSTwAmJIoL5EzGZZHNy751SQA2hgvMUnvPM8hFsM4gmO11loAdVyqSxUDNOb8hM9J7QDoGkgQYY5X8R8iIa/uitahZJHoF6Ska/EttHhe9PPSX1tcleysFW+1tdb2X2gVZOaGSybZW+kCyCQpUaeIW2u8TBBWr4Z6HsFMtRXWqaEUUxG4Jbtr/k3njargaKL9rAxAS03XPCWCCH5hYJmze0v7I95MTWVJVKZGebdrdDpWljhcOBn0fm25uQa19di9Z9oAwDijBw3LVpEIyuRsBuWElkc6UYNYlEE4NLOzGCIU2H4LsBfqWICCQJkxTmlLTI2a/02e0zL59pvQAHXJuQiE9V6RPupyzGDzp+BvzVgzntyxrWuXsmLdRq4cxhIRYnheO+uzSht2PnHnvYAcmrTkhc2bN4KWqF3QlrqR7XyshOrZUVFMbWTSX1kJbAuIQcXEWuRSEqwTn1mofYHMn3tzlXad/52kUmSu3jYhqeHRS2N0AdKIFxmySnDxlhDVg7JATY2jcMyd+9nOF80avu7ua4e9hfz44RedQW2vgljXuRsT9CsOE3eSsCmeVTIGwV1Ds30l5J6TYkWvRJ6kAJxAxo9aFcjZDI5ky1nt+PrXAL9eWEQK5tYbHpB2AGjwCH5uL4eb3PvLM+MAkbknmfKBkzwUPY4k/McroqJjUsHianq8xPNLqMI473N29x253B4D8Sryn782JBGpyqXhk3ROgJYbOWZoi6gRy+u8BmJQYSWk2xhXrjRV/zgneD13yC0B4B7YlboRANq6CPG8xrkqwI1VZGq/rx/oct2Kc813iKFyICbvpDvu9TNENsN7yM1eRHcH6It38WUj3K8/9VwM/BbArmM9uhWr4C1zdRt2YEtvSRna5Mi7qAUk/S5jOAs8sywWXy3EzAxn8oKpwPgW9eD38rnrl3PujTbZVLreOdFlrUS3B5Vr1Xwd/+cMzmOLk19QLu+ClikwE19DGT30gADBRpgHka82JUGAgsSkWS1yC1qzyK4TzIHLIbwRPfuOSCna9kGjFHMldb/QeuW5h7m3/9W2PzViriVhjczslAwkjWLQHenUu4XVIZZhTQfbiBEmjLFQ5NcdE7xy8dXDWquzot65SSe639OdhiNHeP3+U2EX1YBfOguVNmXgZA/YPB1Ua661uc8cBENnlWsn/vOeCGGNY+3ylcadO2S0PGWvXz5akxd+IdrjglLQpq27eMxbO4g1RiagpwUWnSZ+04FRCuEduBkJQpGovOaMubTbdD8QhapLO12Y+Evz5+uHzyeAtyzN5NaUMGzNsqTDB8Lmndt9je6bl3ZcxV+sMxsOEnU6mZOUISAInU0HDbsB+iRh31F44v543BkxE+vIIOagkriQlxhjAWXgAJRRWLfQo5TbJWuIQsJreROhBHQtSF9RrLgjToM50gQmKvZcLGc0EHXt21mtFWyv5EYjLaS0F82nG8/mMwziSMZAnSe6ZP5uSSwqgvZhWX3hSFSw27redf+Xntdr2uSYD1THRkAsVkaqnQpSKM78GhEBExsPhHe3ZpXDi6xS+lxja2rEFQ5gw7e7w8PA9Ht9/j7v3d6SbI7w5IVFnMnDSZQxPlRn97K9NdPymcT5iG7bq24XG3rWdOlqtQGEZ3p6MowG4yNeKstpjJKhDejLruuj8I/U3GPrIETlHFTiQLElIfVIxaU/adra2v0PBzlpLhLtMsrVfGj8sHXNZNmO5sdYxJPawp6x0jaxjDc4Ks76kIsgget7yp91U6icZTrQEKXHeobrmmCZBmCqKm05dKxsxh5hPM+Zx1JG2mDNSybpx1yxyoa33KlK+AlfnlDXIi/SvjAdKb9AYo2Ngeu5OlOqaSEvugprzYhdK1X5wFPQleN8S/mLOGLjPnK608fukh6BXJmd1o2ZBCHg7Ii7df3ePu8eDOvjVSqZCK/M+UkwY15GCfWl2ntLfFF7NW0Js3QiZ6IRN8JT03MBxCENQXQmAq2iz1dxobcTWnjJ2JWESO+uxAW0eXwh7pfNMFxKjmJbMp0XPKXCvXUTDSq6aGPXnT//dKqreKOiW1StfNgJnI3LWCk1kUSogaE5q7SfLSEfgue/IBDnpkUuiBJAFdJxX3L2/B8BiMVG+jwuKjsxXd1X9RxQNMgYulzbmeGuPfxaBMR5dHBxP2zSCZ60V4zRgx54oopQahpa8yzH03APP+1rOiduFzdfi9HzCTx8+wRiDwziSQ2ltSJNhYTDiiTT9DFlSFFDFPyPF2wJ/4RazQ0DtxvE0Jg3Nnhig/TasQZEcYwyGYdo8o94FWOc3cVSRc/6+YZiwvztg/7jH/n6/Ge0UgTcRUvrSEj7B10TLfkPFn1BqaJWzpQxQRvnC0BzwgPaiU0YUFJ6qGoSatOO6tllGCfwpUYCnB4ZmP3037wkhiiWBtZs2tIjdAC072zA0b1jCKC8ATM1KXOs/U0lbK2m2V35BJDM01qp5hev7Vi9nzOeZrCnjQoxMCJ+ijbSIbrRh/oOzNK4j0pSZA0eR2evaWKe/R7pSzm1lp6nlvOB0WLQKTpk2a9oo8jYgXqE54ihl+VpYa2D2I7O4qZIYp6HNpPNLFFPe9jPlutvmU2CsoRFHDvrGWXghCpaCmPNNgV+fLU4ehMErz1+vQJnlODW7Z4nj3Yj9/R77hx0Oj3s87vda0dD5JVxixGVdCVE5L3rdNseSugSLq1y5JFIN9FLNgbkf1VrgBm6jqMdpUt99TZId59GCv0m6kUlF2/tS6PXM5Y2Pgcq7zqRbvjBrvoeOaRMMm+dLpjpkT3nTGvL2qxvgl5bwRZRzIEGsa/mlyBMrtiELQr4zhoJ55fNS9C1v26PGWGJ1R2p5ynsPQBM5epciqvAbOk6BivywIqK+J78j8Es7slYiHIcpwCVH3B2eo6+16r3xA1X13jenurQmzOdFWxUw5JzqHFXicmw50TN/ej7h6acnWEuGZXePB1hjlFxpWZMDPKtP5FhqK4rvgxjfxHVBXBek/Osjbb+26Bl7u3cay94sLCneziPrKOrh4UCumYJEOaOTLtdJWW90FQaP6W7H49Jh44kTF2odCSray4YTkiC8C0ux4vdq9VM12piHRCpzbzK8/iFThbJOY102hMvLGZfj3CrAHLlt0GfXXq0qx3GPEEYVgACrtom5ibrn5dYvlRsHbMetblnGNPnS6xfJcJAvuSAbwyN7Utkm0hAYPMYdB33WUZfRleOnVxyfTji/nHA5BizLGSlJ0iNER4KOjGnjMPJA+CB8gEagk2uyRQtuPHdr2ugiuwSO+xFlkukJ+ve4rGRQkRok3TasrK5SaU0QRzoXHKaNMFHbXN8Q+ToSl7Dn5b7SdTGq3iWJg76QtWBNCdMN5y/IxuY4YoNBxYVLOR7M4BaU6dpOt2RKllLOCsH3wYT6nAvm80wjnzw+JTwZ6SXTZ5XNvc0xa7vHMzwuVfItK4yd2iBDsXodJPgkaPCnDTvpcUmFInaxhHQlnYqQkTQiRtK4by5JYU/vA9K60wBkTBN8ahyjymNf2w3aGPERsCp7+61LRwJZLyPnhriZQB4cySedIdfrkqg1F0LQ+yDXy1iDcTcAu9YizIzgGGspiDKEXwavUxVxMTqyRddy0MTSB0dFjrTXyq+Lov2WVXLTlRDvjDrQdTUWTWyLNfOFqGq4bRPXGfPxwrbFR7Kk7hjyYnlbSsGyXnA6vcL/QoFO9vC0JhpZZnQvjIGT31YQGQdl2NNxFyzzimWdv6pc96v3/sqcR3+fadMavYaA7JPDGJAOk+6ZgnwSSkC6ECJ0JDGJNCeSjvMOOyoOhbwuKJ/srcqhYbIgxeWGIljD/LffG/hTWuFZKUg0eWVOuneQ6qEQERIJU9DvAcjKsBmntIsq/09ogvSzSMRgGHbsluQ3Ain6skvfsbSgQP/csi2YbV/+1nUNL8qYhwS49veCxGS1UpgEs2PrXNahFoc2HX0KR9hng3k+IyUDa0nikUQvBoVupYfdCCacfKTMYkdvndLMjbPMkpnm1OB+6d8B0KAuhDZNDDmo2diU9TK7DWYOJN47nINvvW6GMp306TmIo9Q24SCjX5JJa+9XdNpbwikVdS5106P/pvOXysvQ59XadMypDdLMpURUhfpw0MTUGKNEsxQzlsOCl92IUby2M/2cuJidns+4vJ6xsCXzclma45e8X86yeBQ0uOdUdFMh/kEHN9+wxmnA0lUXoqEgq6E6VPmXUmEKjTgJYbcf5S2pMCdloSQxk3mLELFk/Mg5jxAG7YdK0CQEqwAMnwMNkXnzvJumCHmrOyERTmlzXy4OhhEYdSK1RkcrEZsQE/XsnW70AgkbV3REUe6ZCA5RO9CqDoI83wAFButXmNVwCxCwJuskSbgmV5cmfX7rIri8BVnVpecWUhjTZq+X4g+1Is6k5//68RVPPz/h9eMrLq/kOZ+5Apd7K/PrAFkM00QAtXdk3HN3R0iPmGBFQcK6uAFDXKq4RqwztYoJNb61zeO7uNQUUeV8nSNhLxk11rHtwW+I1aJrIu0saZ0ZY1SQqZTm4ic/t/EwYa2K5tlRW7K1OpTiUItBtZWDPvsifOW5/7o733KB9wM9UJ3rk/fN+Q6APsAiJhMmhum40qWfaQGI+vDt5QnLiGFYOlKf6yr9ZvAjXALTPexNPne7CWy1+m97EWo3wy8ZOpcgdC0EYisFKfJNd1khK5WYZLctgftFCU+Y9+T53np+m5lV79gPPGh2DUC18fU4c0HdiMlw4Lpx84Nps7JCXlvnVbNVmZlVq2Dw+Jqhay0CKDITLdBuWml8pxRCgebjhSCuqUFcWrm6phnRz83LeRljtJ0ikq/OdMY6DNPfsmSUzFkLx2NrBPF246pJqvGszoNkxmT0ni7nBZfjrNbNoa8EGcKX/u/K9tcS+CVwSr/VspqgsrlDp/bG10UqMnoGbrv142HCOK9YzjOWi9PEg67plrz5pg0D+U/D5NiKXN8STIWv4lwTYiKkb0III8Gjg+g4tM9UFKOD+/vfLS0Pa83NiY+QziQQXTtquuDhUobnSo3uv+hJOIVr1UbW8IjpGFSu11y9q5pMxayBhnq6NMEhySQYHbs2ayqpkXp/T6EjifommQ8OwKBtrD4JJfiZW1fLitPLCS8fXnD8dMTl9YzL8cJo5gqVnbVS3WcIp6l52fO7xWQ24fVo8sh7LtAKrbhGsq1dZ6wr2f/6G7X6yc65jdPJPRLtAP3To9zOAa6NkSJVbsE2krsQOfs9XJUpS3u3bFfE6P0tMjVjN8foXEFGUlVZPdbfS+5LOSKnLbEOoKAquuESpAB+KXzzwtaALeQMJnPlTBchjANGVvd7I0/rmiDQtVa+WPHKJgR9CUprGwiL3pqb4S+t5IV5rP7qFrV7eenzqbpURT55cRgKSjETfGUtQ8WNcS/CMyJaYoz8O1exvo3UyM3vN2L5b1PQIPOu8rllycYNYDOhIXCrEAs3M+s8YglXOTBR0pL3oyYQIl9MLytxB8bjrKSZXpZWz5eFjeiibOegdaN32zlwAMhMzLtlifqdswbBNW2GUgr3+tlWWvrZHcQHgK8PqTSGY4PON/3g3P1h1GoT9DtmvbQxKicPogmR5V2zufUdzXZj+tY1HSZKQE4zVWuxqahV89bERNtTCsWDE3hiYEuSP0yDwtta6XSaFsZgo8UgcDuZlWAD66vyY6kgFbMWjKQvfGvS64KDmUUCNsC6tRE3LcHV4j/vAgnMZH4+ZO+zHLDEO4NafBML2tjNeQJoKpjzonkMmWKNm5ZJCAOPwrbpqg0aydfk1uAvfIPEgmOCSNRa4YpTnoLrEnvdDzjRnU/UriLxotSp07VgT+igV9hfyIuatHMxZ2DgnUMeC4ZppGvNrU1KxJveCHHFZkYrbrv3pJjXRKqAbcIpwnM5Zarcc2v1pDUpV2U+idLhykXSomTunj8gha7uadbDh0H7+Zr0Wmq70N9N9zPcKrcyzZG+eu9/0zhfRdUbljPP2VZozw0A4GhszbqtgpxCFAzTlERjeeKcJsp6UjFtzFhqN6IHoPJGQbaeWzan/D9dxBbwpD1w6yKfaJmNFwIXb3ylwKJ9NlXdXSVUKpKzmDEryc09NbdAZbQuUSEsETwhWdimBSCzyXRPBHlpVZ0mRQxFacXDFeItS0cP5TgvC5Z5JejNmo1cKgDtVcMCKE3VTYRdPEu4AjT1UVNqaluXBb6zOpbqSIN/pwVvRUPAGSWfSbDrSVh0nSvWGwO/tRbOGt14PEtT98+e3AMAKuGZeaql1orVGLiwdn4KbexLfe4BTY577e+couqN0yYZEEJoCZ1MEnByKVVI3w66tfAb9yPGM0sCHwci3KW3iYQm2NzG0gDhqertWemtB102kKgk03INAShC1iew8pyjVp3mkWpJPDwM9/eF53Erv0dn1otXQq5U4v0Uk8jr5kjE1eqqHisp8ElCwyiM6G8wuhWmoCZO8mwUbgHENZH09GHkYsMhpQTveRJGe8ZOBY3U4+B32NIC3SjvvCKtkfZr3Y8rF37dCG7teByMhNFod0KtWfcuuX/y7FjrMYSRtOlZA0Fc90T2XEdTfeOvAM0yXfRfRLgnxZV+5y2sVlB7QUAkkeiVe6cyvbEhs1occaIvSKgkPzKqPs8nMu9ZL5oEyd5JrWwH7wd4FyjwhwnBDxAnQ+vJpEgQveuR+k1y8h9HwEdeWoJkFNqVDV+DP72w4Ac4sUa/MTSG05s+yIFazpg0iCmrNRKxh18C3Tgk4/8Ca7VVH0azatlUb1nrZdE+tKoA1oqceMP36B5kPQq+qSTrKRWxQBQi1SoVn2yEQnYi0Z0tG5rEXUyD902bhTemSYU6DrKqgtgJ43zrcsHxiJ4ox7ESY85wuA6AZot+1FYVioUxCleAzqneg5Lk1gTHc8w5ZoSRpzT4GtFm+flz7JcEfXmeSq2IKQG/Q8lMNp7Be3gm9CTDLHov5KaG/pTMyIZwT6o8v5Q4SkDv2znAFj4nTo1sOE43hVp3inRUTp5lvFGcDfsk49Z1t99h2S9qkexPHsk28l7NBdU05bnAJNb+Wesd5eTnZMl+0vcwm4x3B2nXVtXr9AyjLIRACnGuGcO44FRV0N6Y9I77EWmlnuwwBaxz0FG2MLARGfe9o4znpQyTaO+pFVjmFXZNCBOP3XmrOv+CIKaYlLNBI7ML9amFH8HkRs9Qu0uUgO7vdwhTTwTLyLkT0rqx2pXjLLkqoXc5LwjjoEUAJWn0fAkiQ1ym1l5pSS4/07IXOAfjfRfwAqbpgLvHO9y/v8PduwOmux12D3vs73fY7SeVCY+SHBcpIrOKZwlyuCzn38XmB4DpbqeTGUAr0jSoJnpGY60AcwhFu6aXWpfjWdcZ60Ltjnk5YV1mltWNmvBSK3zANB2ozcWBX3huIYzwtb1blRFvA2mBU7Kbs4iE/U6THvSbUSUGLvWcIhN7Kt/wFoCqvsAFiGAWftFeZf+yb4J6bRKzwtYVnevr3pUE9141zlrLYw1G9QV6xbNbVkok3gFgMz4EHu+SCsCFNvergiQM3fYBMzP0JSzma3JSrc1tSSAc5zy8C+y41UZbVLmPM2PZ9IVtq0F3vC3w++CRatwI1eTInveDB9AFGMM9RzT9BukNjvuxke+4VWC5Zydz/kBLIPUedxVs4DaAKBU6TyQvYfz3yxiq0mutSKVgjbcF/qELGs6yJj573utUSSo08x7ihnyac2HYsZl2CMyH2vFlwFRp/jcljPJ1lD74EEbeSANqHVTcSGxwnXhEKMGPIcQbg/93hwOO54vanvYTAgqvdwkvkb4GTIexVWpcKfdQdM87kH8XlC/FJnusGvxJRG8WdoZLOh0gapl6DLbZ/Mo74MNtCd/9w4FHK8lWdmBWeSmVRtxEY3/wGMSlE9BxzMvxolX6sBuQ9kmD1DxcYJ2Yn7VEqlc6TSnrBIS4PFprEQ5EGtzf71uRxf4FinpBqsGbTl0FY8RQbGWNCZrIod51BjSh8cHBcCjZrQnLZcHlOOFyvKjXgDUOpQ76O+gdtfCBSH37hwP2jwcdZxtYDGg3DPDO0TRMIalsUUFtipkRTZ9//t1yzSMLN0mRpWPRnMAIr8CYNl1Gk09NVG2ZZ8zLCZfLkQL+fMK6XpDiSu3znFFrQ8Lkuqe06iRbCCtKyYpglWJhs9EElC8kxzjPxVYTBfq19dW3wvkAZ5tQQUor1nXV/o8fPLzZBtmMrNVc4gdBXM0k+AvxTaG72swWeqla8VzvAyRVdQQhB8OMTwt1CoNtMHOrQm9Ub8s98aIpl1lngZSRTYPTh92wkeeULBBggaGZNJwl2+t7XqhVWyryb/SwFe3dSBAIYcAwTNjtDgBY8Y0ht37Dk8To1sDvApG6YETAgg2QCpsqoVBllRxEtbBnKtN1F/c2jzBIK4aOSSvH2mbSrWedCH75p8PUJEF3g0L/ck1j7EddurYLiNQXmXyH3bcP9E1hQOo0BJyxCm9Kj1Hg6sAmJZKc5pxhotFn2zmvI6me3yljG/QvfTltBWRSH6MX3yH4gQRQ/MBGOEyCFNEiVi4UVzrtTeK2ze9xv8d+N+E0DWS+M7Rxq34OHeiIpZWComzaYfAq7Rycg7dNn7/nOaRSsMSIJMgW80b6frFZqccvyoXr0sYbqe3T7ICFHxK4XXTLen844Hg40x7HSY3sXyLM4wfHff7A70bTrVguRDIzxmA47+CfienvO/OZnrQq16LXNWiM98AiUBPG/Yi7xwOmw6RMd7FvFsVQsQAO0/DF8/u1Jb73W0OxrP8uBFY/BJ3yGTyZRNWHomOtfRsrLlaRTIX7jVFFTmNNS/IuRPj1wZOjnbVYY8LleFFzs8TEWTUqSkWts6Ut5m4k9437EZhX1YqBBWm5dAVGn/hT7MrteZ3PrdJniP9yOWJdL40jZy0AC5GZ6JE++aOcFeN432/+BRtHRksy4rUP/L/XpMf7gcRijFjzUuWyzlFhajCEY73VGXuRrrwcLzh+OuL8TP2NeT4hxrUjObTALhseanPCspb7Huwv7X1gPWMDw0FftO3bhRCRhHZRbyW6XJOJNuiEtaiVKj0wzHmttjSfFvjhskEmKtpMKwX7Vlmqkhm7L6WUkNe1PQQ87QAQTObXgLpv40Cu74+JeNCNm5/A80KklOshZB84i8Cb/pqzVivXpiY9pC2oRE+2vDbr8QOZD013O7LqZHWwYRoQvCP4Xg2Miso5q5sX9+UlqPS+9resXAsyJzDBUdsij3R+VHV6lN2oQk27uwn7+x3W+Z5QMSY4TocJ092OxpbGoJu02I7m1DbbtNJGdzle1CRJKj9VO+QpAcckW8t8CmPtG67Dt6773Q4Pux2eOQGTQFpzQdFEsCp6F4XIeNmKeQkiFL2MQ6ZNsic8HuH3SDAUMqkoRoqAFJHfYqskpZ2lk0RBj3fYDZjG24Lf426Hp4eDtqT8kOCT9FYbCiXkZoARQZ0A6ts7RDorx8/ryzdHtjbuRnvegGFg3Y/7vQpB7e73GHdkyZ1jgmElN/KA4D64JbngW5a0ySqPoIlWhzD3ayFRL8vjvcM0wHFrwQ8Bu/s9HpjXMZ9nnJ/PWFeqyHtym3MeMe7ovneQt6xaK7VaLY2rxmVtCETXbpbAW3LqUDKHEG6793LdRJcFgAoH6eruc/OLaYJe1jiG7sFBe2znqFMN7RnpYxRV+xPGgSR8d7t7jCwYJHvntWYKId1F43T5jPhQv35D4A/MUhVGc0KM5Mkc14gxjxyo29hYGOjlXWeCoeIcMc9nHF8/4Xh6wjyf1LKwz2764Ox4ltIaizBMPM8+YZoOmCbwrG8b8TOG1MWEHU9GEm0D+sp1+OKSMab+AZAgXF1FKQYuZKDQKKPM6Et/fLpbNVMfp4EIH/O0mV4AGuxJG19hFmzEwr2hGFfUQp7UJGPM7RXpqbk2y66wLzPih91tL4CQSNpD1vgGAJQ0KIx2ISlKVi6VTK1VdfkFtoJr45biOiatIqn4e8evwzhi8B7OWsSU8IILFkgiAhhAP8sZIgSJeI9U59+6lhjpc7rs2nOLxUffWPn89cBBRu6jMQbTYcLd+zvcf3ePh8Me91M7l60zX8GSIuY14rQsOC0LXl9OeP3witPLCfORZqGF3W0MiX0MY2DbTtEw6N3tbmf270Kg45wGDLsmyUp97IaCKEHVtBHP+XhpaEZu7TyZCol9pcYIn1TT0trRlklHDgSgiEBJmSY9wBup59G7ka7JIERR726aad+PIx52O5z2F6yXFYEre1lO2isbLQmH3d0OD3+i5ERIbmlNOL+ccXm9MIrZO/Q1mWWAWibjbsTunhNe3vClly4y0GEIqKUqolhzUfLbwKqN+4f9Tfdepi1MMTwbTwS1QcxzjNlIebvgUCa6Hzk2xGa9UKCezzNOpyecdO9vCY7s6YfjIy7Hd5rkxWVtIj7WaNsnrUmZ8roPcxsyseJrCJP2zG9Z4zR0lTwnqaaqUJAgynSNqrbtXGjXnlA+q8+oOihuxtJlv88bhFtGCZ2zihIJwVnam82/gyTe6X0RBDHpNf7S+jrUz5AJ9fAtw/1JxQnyHUu1yjVxFsbSC0IKTBFx2fH1IvOA4Acs60zZX4pIubnPAeh6KZJJMyGqm5M0sBrkAQBS1MlYXGijgL9nKaRbemiTq2/+f3rBReLStJfPGoz7Eethwu5+j/n9HT+0UacdgD7oN+hY+t8i7LIsF4ayilYEAmt6FsVRS87geIaYNozpxsxf3LlUXYzJVoUnGyi5MnrM3nskT14FcjuapDIjOK6NmknAFwKWkH/k+onO/RQCVdqMixW5VqXNwBrP991anb+vhfT2VfTjG9dlXRE6IhJAvX7RJygpowSHnDsVPm5VSFX++P4e/+K77/DP3z3iftoRQZCDolTjmZGJOa44LyTde15XPN+f8eHxDi/PR5yejrgcZ04cabRMk6mOVNVXlL/HnW/wHvuBKmYds+R59lrrZoSJSK/U/ptPpNEvKoRyzMtl4QR21nZXyQlZoc2iSJ+odno/8LMeuPqduhEm0HQHw8RNCpvHAHlenirRb0d89sNAiQ+3lkQuGKDASFoTjTzsh4Dd3W6jVips9/VCbnskxrR1I+ynbwDoOKs8+4KibqDzLvAAoqFfYJeoU1LDGG6u+AWtQIIGcunzexZsq5U0OM4vJwDAOq7k1zBHmuP/5RmffnzC809PeHn5Bc/PP+Pl5QMu5xes3MIyIH7KOO6x3z/g4eF73L98h3fPP2A5v8dyWbG/3yNMof1OTiaIX2a1uJPk0lqLYeDAfyPUT+JLco9aSynXqgRl5x1MNjylZmBhdb8VboBOJnWTCH3bmP+ixO64RCRGbwQNkz2lT+rj2r6H3nduoUH4ReTe96vn+LWLMAyjwuytL5dIC5khXYVclaRgYbj6kZfi7n3Ecn7E6fk9VS9zYzYm1QlIG5i75IyKQsxF3RAGNjxoCoA9ii/knusZ3ltJrjJffI1K9BmWiUQ2imvUSp4ILSSwMnEWPx0mpMeo1Y0cuECmMtMshEbJqi/3OyY2xY3+sx8Y1pwG1aoXxTHZrAeGzG9ZA/MGSKDGbTa+WopyKAIbp5Sut++8Vci/bxX0i2bCjQqFAEAdquqPk8d2xGwNcilYWNxojitWVbRrTnguOIycJBhDG4pZCwAAzThJREFUPyMv1C3rdZ6xH4dmQWwM9fnZqMolD5ty0xB3TTJXXMrupglTCPAsWLKmhLkWLUJrZS5CTrisEWtKWFLEEhOiKqeR2FO/GUiiJZuC4QDSr98T+McQsBsGSrokmA4BzlOLr6DvS/J9X+m/cyaHvdPLCceXZxyPn3A6PauIixKcUlReS89JcD40JrMPGMc9drs7lHKPIUzwYVCCq6ADshl7sZAdPIK7fZJj8J7c4TxzBnJgMStKakSiViSNAyv1jazKuAsBd9OEMXjkUjdckVLrhtxpDU2fpA4BdJaetTVnXNYV53XpfDFkxNOh+LyxzSVDI/KIECe9b13yzsIzwrI2Pw4iTjqdZphPM0quig4ulwWvH1/x6cdPePrxSQM+/fkFl/OrJn2Fx5VDGHE+vygZlkjBXpFMoBEJCWUjzxQdqxTkqBZY6zGOnIz5G7lNvmk00D1LCuEXla4HSzlb1FgBCwQftE0CUHUve3DjfmUdwdU/v4JIyudt0LvaHCmBhrRnIR7m/wgVP2XdXmen5ZfnwlrbvXpUKajVAjCsJz/CeXoIBfK646p3nVdlrUoWLPPLMc68SZCXsVwB6vEPGIcdvBfFsq24j/S5RTb2moj0rYtQB7vpxdC/C6nCoCSjEPdyXsh/nitiyehhWGzGDHAdiUcqV/X27mBaAAiVID3vnfZA5R5Ya5joNSjJS1jnJA1MX9tNt20AYaRjtdxj62dWBcb33qEOdfNvzlusi4dXF7ImaiPfY4xBMVl73Azy0M87hxyJFJpzgZ/XjXCRGLqklWBTeVGHMWAKAQMz+Fd+5tb5Nt3u+UzV624Y4CEaFVZn+nPMG18A7e3mptj30RjEnPHheMTAz6RwBuRnqOLPSJlaE0kSaYbAkyoCNoRIODVSCch96RNTSX6UQfQNy1uLwVMiJZC2BDmZ1e+fxbaRQSda5Fh7WNtaR5wh6+Bd0EkG0wmYWJYdFRKktVZJioJqyUinEBubZnzX9uB2zy3LO4sxUPAfdkODlRnFFLhXgv64H3G42+FumhQteNzvsRsGFYIavFP7VNtdl8JJrSA+MWfiseSE13nRhDGaxONs3Z5mGpFZtBSMMaz7f9soo+wztvC9zaInT1NMtOeMijQINF9rJV+OZ25NLWedW4+RVVkl4bEOtkBf+loLt35TG+/k6Shjmwy46IIAYP1+7qvzvjKEUcnQ7ivqdV9aVGR6YIfWjo2pxZuOtGitRels62sV+2XS8piZfyIaBeLuqXt+yjq6qVMjMpUm+hic8ItNsBSX1ALBJuGvjKB9zZL4q4Gf5DMHHiUT2N/zLynaAxdmJVhxznPWJvK9wtakTYsyoY1aX0duWi4e1nrEuLSbIZsdsxt79rxsksJ4pIejsYbFTeyWRe0NIiGmlCDz9bQxUdadc9HeU+DMN65Jdbr7TVmJKDzBoJKNHdFJroVA7LXWzXiiGo+YJqKhLOYhYJwGjFx9DDuq2nDDVIOMigms2CMeAgf6YUDgc9N5ZUs/lzyJeCSbgAV6vkDXf9a8biuvSvBXboEkFUUCxOGtCOwWiAx4GKktYK3Fyo53l+MF59fzN587AFyOc9ukh4BgPIL0nktBHjKPOVmkxDbJqaE2aSUZ3pM/bgiMpRd52qA+3bPQc0mqzLA3zX5ZwuDue4Z07yz7C9ye9FpDLocimX2dYFSu/MUGtFqRcgUAQvwcQ7l3d++xLGdNAHvlMpk537ihdYFNEv4hTMRvcaKIJ4mP0xE+H5qjXi7l5sTHGovRB0xDwDS2wE/PaSs4BGlywSF4j8F7BA707fxoFNRbp8ZPuVb1kyi1stsltXzEW0KQgiVFrKxOl5nUWkvZtMhkfwxjYAc5d/O913N1TZsiJ6m0LYbBYf9I/IF1XigBYCW7JBM2wesc+jjuMU0zai0YhkmnmfRaW4dx3GG/f2imbENoY5mu7XniZyCk5eWy6HPvfYDZ3fPzGPA12dovrcAkOptoagL8+U5GGXPRVoMoNOok2hqVfCqkZjWsM0anwiQuSaEb10WTIiF2hjAgVBJOcqXFEUF8rHewaBV/jBGFE6h1nX/1HL8a+KfpQD1LP3KfbWTJyKAbkszeZ9uYhtXZzctCcAVDFyKnmQqKZHzCmO/GHXw3e92706mxS23kiFobzN9L2sro4K2Lgh47LeWks/dysb0HcoaSWS6Be5wxqXVjbw26ESFhVybdzGuz0+1FTeg4BP7ihIqvoYzvSW+QGM2DtgCC87dDvoyg+KFVdSIhWxipAaMNga+1YWTD+saxoPFHg1otqunnuU17HliMSPpiqletcGqDuWTPsNbAivXtYYeHaYf9MCDXgkuMOJ8ueP34itePrzed/unlpNl34HElaiPQtUg5I3H/N0Wq2CkhApwGdGyMOno9in6y4ZrcKhBIPwcv4lFyLTQQXakJWlY7k03nlrWkpEGo57cYA61Uci6wtbMDZcaxCOeIHwWx9h+p9dOpKGqbs2dI8/URcqvKd1vPs+9o43uMevTPiQSrUgqWlX/+8O0kN21ZGYvgPfJYFHK1XdUt42gAuGWTEXLGmpImH0tKOM6zBvpUMkol3pe4qMWcqYUlolW16s/Na9RRNTm2niOggd9bGBOUZxBvRLqkOPNXRUvJlOjI5JK1FucXw/e1yaxLq6G+k9E6+t5x3G0I3f1o2zDssN/fY79/xG53x8ZlTtHS1kJ0GPeTIj2rTncYjOOeEwAKmlIofOuaDhPE9EeY+qJNQyOUW/tkITxKwSbaAkrw84QQ9/A+OtRGLNfBE3L93ljl/UsZGZnF44oWgNLyyjljncWgKyPG31nxHw4PMMZhGEb0M+TjSONL8qL2M5sC+emDKuM7rIHQvMzlZ7NadcZ5pcwltzG/N8zkUlUvXH6/EmVck20VaI5+z20PgR98m7dn5bVSkgrEABOcq4jRws5uQ7CSZUajsFutDOOUirQ2pmpKSaVLe3U0gX5Er9wYCvoirCIjRRtS0J4MTvzvhDsBKLNUNnUd12OYr5SCkVW9AMC6jGSbg1pOGXa1Cs9Jb6oP+P0YovhWC4vZ85SCwsulAoYTCe/gx4DD/R7f393h/d0dvLU4zjMu60oOYT894eWXl5vO/fXjawtiweMwjqzdzxt9bWx0anu16yzok7UG1dB9N8YAjvQPCnWQdBk0P4laq44n9oYolAQ0sqEQf8QatKFiLVELzm1JML9xfTod8XQ64bwuzXq4a03JLHfmDQrBq3y1HAec6xIgkdvuWgId3KliPfwHq8ihcqBDQSmmJcL8rjdN/F6zg0cCCwnQ3BL4j8uM07JgSQkxEWwrARFjz+4nNMQHnmOvFalkxNwC5pIScils9NQlaBz4Sy1IuShCkUrhSj/RzzJr2zmLkptgliBxJF1tEdBY7JKc37KMkT2U/ruvUgEoWVj0NObTzEVM5zjHLa9aGr8ohEnhfHoe2qx6CMTu3+3uMEwj7Wu2+TMkbqsJedE52/k7EN9pLHtCV9jx9Nakd7rbURFzar4FZpXpCx6ni4L89jyyt6OaUiSqIyMXePIO0x4aMKRxU+TJPWhIYBsR7a/DMA0wzpLJ13mBMZZ4M79Xsvf+/jsAaMIjrBcuo0RSffeQo76MstkDqKkFcqnE2wMirQKRqy3b72VY7FqGcvN18YTuXi56uGh/zTe+BON+JJWoKIpIiUbralWih4yNmLk9HAJ3ywgbSV5CNzhR1lI4bQZSichpK2VaSwW8A1lPs1jQEJqUKiMKzltWTpt03t0YgzUlrAlA+Haii/y+YTfo2FJcPcxlaRbIhe5N85cXxim9HCIqVEtBrBWmZE4KsVF+o3MQ8SGn6m/CXTAcPGEBB9ey/P2IHx7u8cPDPR53e+RS8Dpf8Ho649OPT/j4Tx/x6a8fb7r3p6cTJyP0vC9jZA6BgzF0z3P3Qlpnm+kSZ+LGaPH+ZpRHlm4GpQVEWfJeSDLYP9uAVL/bsTbjLEPHGd5Z4AbE96/PLzjOM47zwqO7zNdQj/jrsTQab9Vj6wJ83+JSyW2g9TpZxEYEcFKKJF7U9YSl5w+EJgkrhD4vED898yllgEcf5+MF+Ps/ffP5/+PHT3i9XPB8oTHKxD1e55s74jAEeOcUCRq8R+DE0BjS6FhT0uQ7ZaOJo7e2JQIFkPhxfY+dNRh9IKKfIVVQIhn2Cn1kjWuYylNy1Z77LUugayLORiKxqWZGxeA9dsylkRHMdaZZ/xx7DoaHHwr8EDGOO1AfP+HaRIbO0ymSrPys2nrhALUeZd+rFTi/nFFyhmMUQoSrxsNEselGpJOmMWxDVq9atfIsC/JDB2daT34i1IUQEqPFjBQvsnrkTN7zrVhcUZS153Voe/MwYdpP+u/kZOl5WuLXQ/tXA//jY3tpZBOWCtQFz17MXR+wq1TkRuRkUFxGslvVrvb/0P8mjX2PUjKTP6B9vt6et12c5gHvriDPPsm4tdM5HSba6CJvRqUQUYWFjFKKDDG1hEWd4oInf22BK4OHN0aFNsRkRrTO4xoQ2I4yLhE2Gv05IuuNOh2wu5sw7EblNIjz2bSfMHKQT4qkRODxtsAvgW/kzHLgYL7Oa4P3eBOroeo9yTFxRUYQZIrNpVEp7QJVcvDqN/TrHiN/e1eN0LG92x/w/d093u0PmELAZV2xxITT0wkf//oRv/zjL/jw4S833fvL8UJz7NOIcTdg3k045IzRe0zBw9ntjP8aVjXv6AMEIK0rp5r/1nTjfEz2o2SSAnbOtElm5gr041x9FaAtEP6djufWS6ZoQqS4b3/6//LpEy7zoraqYtai1Tm3q/rNTKSCJbmVTa0prcWNeptIltKfDHEArSUjl9Y2dC5gCCOsaYx9SfStt2oBLip9y3nBJWVyObwR7v6HXz5gPs86TSM93YlHc8ch6MSG3Ecv+v2msfUB6uEbGAzCAXAO3lkl+hFKQFX+DGDtJGe9bSOsgmACbY+BMQgYNm0AIr1uR5C/Ze3udjg/n3QeP8UMGIPd/Y5G+1LC+wMRFzVJfYI6+YmPgtjSapEA4nHQ9zS5ckleKkPCBFtHuLDqiCZA+6AgmirfHLP+O7UGLGl/7MebfRo00bDdHL4Uq/xcV93Ctox7ay0H4Fac+JGeT/FVAYTDlNT1UhAE4nQxKp6YV5YzS7jTu2DMoHu9oC/WWcyvF3gXVOvl19bXof53dxRwbRNboetQm3XqELTC0flW2+xSZdZSCFuSPfarVigEYkxGKZ3nM0vP9rCKQOHy9Z4Y1gI+zVP2m+a3rsPjgdiYiQyKhDSxxhmIM1JaUEtGLfsNdCXJkc4VB6r+KIvsXccI4s5p0A2SZDIXpMjjXIEkQ4cd3ezd3aRZrRIaWahHxs8SM8VFZAOP99987v2GPuyIL5AGynStNW808sVBK+esKnKWoXrXBy7bEaWu7h3/YiLGsBucsGatowRTJkxGH/Cw2+FxR2xqawxe5wteLhc8//yMj//0ER9++Q/49PTjN587wA5lPKmxnBfMy4q4y7CGyFrOWoVo+x69bmYMAcvcvpC8gqPNXx0EUTWBEBvhmDMWR8YkAKiHmMS5jf3aXSNe9XyKbAyM42t2Y9Xz8z99QFzIWvT8eiYtiTO5M8qUgRjODLlBzNISEgMVGQdLKwt/iWpnr99Rso710alKQSBiVVTB+DBo8hsGD1hD8+q7EcM0KqFtOS84PZ941Oy29/7jXz+q3LiM0Tp2wSPiGolJ7Ud6L0opyLVowJepgkIRWAl7cn4S9PvzzYWmOlS+WKD/TOOeEgQA8NgoK6r6ooRhQVDjStDvLev+u3u6hq8v9C5fSBl13I944K+ZR4OHHcH4uRLxdD7PyIlGOeWdWc4L1mXh+56Q0ooYlw3kbw1NetB5BbglaADN00D6DsawQFEgAaFUdJ5dFO1KpuTs8HiHu/d3SrT+1hWXqO0yNRvKlZ75JWJmPwZyWGTXxW60k4qVpNo2hcnf8nkAFOkSXpv8f4qZA37Wd6SXbg6MiE6HCYfHA6YDwTzWWZx2I7v6DV8lNv6GwH/AyJUl0Hr48kIN4hBlhLzXKjXrmkqbsdufs85ivep5AWDrw0aoqFUMKii7RW16+XQhm/jFl6CtHBOWGzP/xx8eSSWLM9EYVyzzCbVWfoDb52YmASo7WTYA1zyzfS5KPuxHnqy1QPBE7rBGTWysY517rmrG/YhpP6k5j1rvBkczx3zDM/dhRev81lUrXePR06hcLoWCCYt1ND4FFPIvLO1ai7DU64aNrhwGQWxyQbFW4VTpY/X33TpKKqDJjsVuGPCwm/Cw22EXApaUcF5WfHo94unnJ3z68QM+fPwnvL5+uOncc2aZ0LltYvMhYs0ZE5qo0OAdYraseUCITcoRNjqUISMHVqF0FilnDL4gujaiBoADH7o+r3iiJ626FPIv2yRD3hFBGwDqPedabuZ3/PwPP0PU9kQ2VypAqbbW9aLvr/MWpdv4RFSHCE4OheVEJbmXQK/B/jMjfc46tSedpgN2d5PKN/tAbb1xTwhYmKjtWFLBfCRS5/HT683TPM8/PyHxJFJOguJ4HRuz1hLnwzpMIWjF3ghbbBhkgNwVMakUFCZe9cGfzKSikiqXGBFzVsKgJE90b0WoiPrgcYlE/AL0/bm8XnBicZ1vXQ/fP+Dllxc8fVxxPhM/JsYF3nscHg5493fvUf95Vc7LHCMuu1nthVPqEublwiN982a0L6VVJ6Sc9Qh1hHcekZ3phjoocmz5fMM0UMHBHijkF0DXQVpIw27Ew/cPePzTw0Ym/VvWcl6Uha97Vik6ont6OTLx9A61jrRPlUY+5BsBgGPVmrpj3vJb9D3moE8JctO3KeziKQRJFxzGA0mC3393j93dpLypcT9iHPcYx6/rtnw98D+QbOowtZ5JrVUzExlXk0zT2LLp4wGs1gYWNimtOhDCiO/7F91oxPUssCQOFgW1NGe+UgpMbjdJsjSBISUA3rLe/fCO+0XNeGeZT3DnF8zzEQuLwxhYZPYyoJtFzFXd6Bj+HHYDBzVSlmvKdqVDPISk1ZjuqmTHil6B74dAyH1/UYKHWENejpebzr1P1LyzmELQnqvcF8+Qd3Ces3eqeOQB154VJwKNuFg3ny9VvoztCYohiaQQiYTBPoUB99OEu5EFcpzDeV1xXGa8/PJC1f7Hv+Dp6SfM8/Gm8xcEhkxXyHnrtCy4nyakYcBu8BhDwBwjvCXVwAVQeL7WipUJimKlrCRUu3VPu+6Fl77n3dk1C4rVIyaGg75JRquj5CxcKki+YPOLfuP6+R9+VlXGtMamj87ueTGSEA9AWuQpBoSxEeCcsyilwiePFJImcd6PEFtiEuxqibIxnAxJ4OexrGEYaLN72GN3t9NZdRdIIneYBkqmWcL2/EqIz9PPn7461vSl9fGvn0i0pofdgyc5ajakst7i/eFACn/OwXFgTxywqeq3sI45L/yMx9I2fNnXoiI9SRGfNaXGeVICs4MLBmEM6kOQc4ZNFnDEaYpLJMTj9bb3/rt/9h0+/tNH4C9QV7l5piRi/7DDD//yB5wXQnvupgmP+z2e787EBRISW6lIKWNdZp7nP2NdZqxx5omNVgErL4sNZgyYuzGQJsmwG5iwzC1MbhkZa0let5uw2D8e8O7v3uHddw9Y1tuEu45PrzoimrlVmmPS8dz5csQihjvlHuN+hAlclObSxUlRF61aANVO5+L6GcgxKypWS9EJMkmEvae9//BwwP13D3j4/oEnEOjzdnevxPEadnC/t8c/HSbcvbvD7m5SglrPwAcIwl9nsrAsqSD75mJFLEjae5pHPFWoOTiU7LSKkQdBs6GuHUCsRiixxVgDU0wLFrbJZBL60KBP8Ue+ZT3+8MjjK0FNMS6XI15eP9LI0HLmm2MR8gixViRoi6YTBKFQ33nuRYl4DbAljvT9ImMtZ7usPc7OZxIIvaVxo41Uba0EFZ8Jpj2/3DbHLokIQGNNoi9fKxS6NIaC/uCdVqxCWtrMrpc2hhdXo71iOf9SSMGq5AKbLT9H7XkBoMiJDw6HccTdRMp4wXuUWjHHiA+vR3z66yd8+A8f8OnTX3E6PX1VzOJLa50j/BCxXFb6c16wXhbM+4iUCfKfQsDZeww5c4/XaLJJ87bLRkXyGs6Wf9Pqt9SO4d6Nexb2JOB2kWdjHucdLPdVNRnwGTZS8F+9u4nY+dO//0mragDKthc9gZRWheqdD0jroARaaT8B4ACQMOwGFerq329RrOyvi/5h1HBgffqJq33pnwadauExuZQxn2YcP73i008f8fHjP+FyuW2U8/XjKy6vl04T3SjXZjkvup/sdxNG77Hn6lfuZ8qZnxFi7jtrSVyFvy7vT2UVR/n+nuuhYjeGUU1rdIx3HILKSXvvUQORZ9M6kzHa0xHH59sq/vf/7D0evqeZ+pwTTqdnnI5PKCVjv3/A009PeDqecFoWfHc44HG3w7v9Acf7UyMXs1FZYZMiGlFsSZQowToXEPyAYSRTmhAYrhZtEpa89Z44XsJdEEIjSQtTgSWyye++e8D393f4eLzt/I9PJxVDK7mQ5DR7TKzzgnk5YZ5PKCXrvRFdGX2Pu4JP0U0pdhjm75N9KhSp2t8mwwbOegyBHEoPjwc8/OkB7/7uHcWmEOjZWSJZGk8Dm/z8umjb1wV8xoDpMOLu/T0Odzt456gPxU5JNO4QYQwwnxYICzHZTumvI931G54EaLIZLKiVpU+NQOO2cz7auhHpRe6yJ2HTk4Yz983YJ1lgsm9d797dI93vuVInGdrTyxnPz3d4frYEWfHmMI57nnxYkdLCcBARM6TSTZGEfZT/0J1Lf12stai+wsO3yj5sVcmsMSQawuiAVPtrFp30C84vvyPwyzXWuXmLYO1GNx8AW646/XuttdOkl8+RzzAwdlU1P0F3ul/YsuYEwAOmGDgQjOyDw35oQX83BDhrMa8rPp1O+OnDE375Dz/jl1/+EU9PP+FyOd481pMTJU9+8ApdXo4zTncL3h0O1N92Fjt++Ubvcerm7uPaSDsykPJGrrNsx3t0dKoztxE0CIZ72ntJCul5Av8uGeUTYZEUM2JMNwX+Dz//E0KYWLnzmtWctWoj++AZ3rXgL+2/XoNAkpf2OU27Q5PALukF2iREYMRLxrQAkpW13rWxUd6gXz8d8fLhBU9PP+Ljh7/gciPas5wXHJ+OyClqwCJ0bcRxdyThmFLJS34Y8HePjwp9yyJhnsYPM2DomqIXfw8ANKRM9BdIfMmhmpYkFH5egneYhqDunsGTX0SdaU8+P59wejrifLwt6fnTD+/x458fcbi/g7UW83zEuszIJeNweMSHv/wzPP34CU/fv8f9NGE/DvjucMDr+3vab14vWE4zhtcL/GVECCLFzgS2UjSgidW0QNTDQMZEEvDDENoocLdPOBZOQoROk4jHBwl5DRjDcpNB08wIaWDhpvk0YznN5FIYF6zrosZp1tjmmyJKiXyfNKEVJNq1aQx4aPDfEls79ItJos4H4rfsR9y9v8O7Hx7x/u/e40/39xicw5ozljVi2k885eUxDL8O93818FtLc9y7w4Tv7++wG0a6GHHFcSbok+YHSc1KxkhSTLzJN9Zjm90vG63h7S80MDzeUqtBQUH9zPfWUjsxFNFrZzETJWQQTJlkNviG9bjfwVuH+90OfvBIKeP8fMLTx/cYhh1di/XEmW3EMOzg/cB6yW22W1sPpSCGNqHQyyC372PSn/EKEX3x3ryp9BPO84Lz6wXn5zNBfjdC/ZD2SjdbLJtY/zutkTElo33riqr+63L4xrC8pDWdCllpY4tS9fW61Ghz4eJ5fxjbH2kxHJcZf31+wi//+DN+/oef8eHDX/D6+hHresF+/3DT6Yv72XoJ2jIZdgNOdxPmuzuFJcXQJuWMaRwwd6zeuEYd01Eon70J+qDew4DyNZF01iqJjaeCVIXsQS7tANok2ztgrUFaHXCDSdunTz+SipofSF7Vil+B0/sLrlTWdYZzAeM6qZOe4QTE+VaRA5286BVfR5LAvgrqSbK9CmYvniKJYloTzs9kDvP04SOenn7C0/NPClF/66IR3pk91WfuSYsJDLHbnbM4PJJ7pLzH4rwo/fzePsEYAwcAzqEYIv5ZkNhT4okV0wkcDc5p5S8oWy6FWnqmqRMaY9gNlaDoM/f3l+W2hP+fv3vEP/7pkQhyfkDOGafzM1KO2O/u8dO//xf48d/9hO//xZ/w/d09Hnc7PO73+PPDAy4/zMoruhxnrPOdnru1FikFvY4ktDOpNkwIk7oPbmynfdMHUGTYOzhOkG2lCYfA0x7KO7nRoGk+zYhrUlQ1LivOLxdcTme2ladnQpLBMIwYhkF5SOLpsN3TeOyd0WGTuRDOpE8hy1Dg61BfMmQbpkHR98cfHvHnd4/4/u4OzlosrFJKro1eE6lfW18N/GK3uxsGPEx0g72zWFPGaVnwdD7hOVz4PabxBVFTimvSdFdmHrXn0VU5m99nDKoFTOkEgLrvoyqpE/8pGca0KQIdlxCIX4xibgz8dyNntKBeXs0F5+cTPv71E37++R7OelzSUY0Rck6UEJSxkVecUw2EWkja9lprvd1o6WkTtF26ivBz10uZ4QwvnhcyR3n58IKXDy84PZ9u5jfQhlKQlojzuiA4IjJJBeIYeZDvDc5vREr6UaRrlTrpBaeYYZPZQL7CgRA0SPwHxt2Iu4n+HMYR+2GAsxanZcFfn1/wjz9/wM//8DN++fFHvLx8YDiufLXf9aVlHbGH13nFfLzw2CUdx/PjBT+kCO+segOISttyF3kyg8bJEsutCrytyU4uOsOr1fRV8Gv9ZdIOkOuYU0bMUWfMK0Pwoh+hCFsfeb5hnU7PiHGh9wpEsKKkNnQz9XScMa7wfsEyzxhmakWVMQODZx19v1HZu0btRJp6o10hGyYThFXyNFflO8Cwh0SuuBwvePnwgk8/PuHTpx/VHKaX/f6W1SaRMpblgsvlBes6w8DAhwGlZEyHEfff3bOLpVFhp/0wdE6SnMhBhIgqwf/OKhpQKuAKET+1XdNV/8QPoJHPfFUIVLS23ny84PR8xvn1jBhJzOWW9eeHBzz++R0e/vSA3f4B3pGI2fn0jI+f/oq//vXf4P3/6x3+/J//gKd377BnP4L3d3c4f0d8mPk0s4101MTd+6D24tZ5DMOEIUxU0TKcL4ZUu7udKgSqEqv0yssWGVJpcU4Q5hgxrCuZet3Abzm/XnA5XrR1nFPGfL7gfH7G5fyirdxSiIwcPOkPwJLOgA9+83zreLK0dkuBdYCxHtlk+Nr4bKWYLum1lFDvJh3hvntHFt/v93u8P+zhbeM2ScJE1vWHXz3H37wjeg7+97sdRu+RS8Hjfq/OYyLtaUyr6HSModRGxEsCY0qPd0t06JfeM6mGCs0EC4Qqs6CeTVoUWiwFmUUs0ipV5W3s3jEEPO7oPO/GCSlnnF7O+PBPH/HLT3+HDx/+A07nZ60K+gp9AJCdx7ouymq11hGhkXu05CTYiUQ4ggKLtWpSUXJVWWQlhqAFXZn9vqwrjs8c9H/hwP90xHojv8EYQ3A3VxG1kmuZBHwRLaFbJMmAURlSGzxqHZFr6XqadC+NtRSofEZJTv0aAGgbRAR8hmnA7m6H/WGHu5EIffcT6fIvMeLH52f8259/xk//9kf89O9/xqdPf8X5/IyUIpxzGMJt9qQueNRKI2nrEnE5XlSg4+nxFZ/u7jB6Gj0aQ0CpzMBmSU9R9EsrKciJfncv2iEw9wby7pIkYccjOJVBFiSLuAeLMs3DmHXKgxCB26Wqz+cXxI4Y58OA3S5yO2tA09cnUatlOcM5j3AinXWn/vHSH3ebql30BwTl6K2oe24PuiSBFD6TSv9KgpBzwfHpiOdfXjjg/4Lj8RPO55c3Y8O/dUnlVOsR63rB+fyKZTnr59VaMU0H7B8Ob4SZvjscMA2UGGVGJNvpGDgrFakEeaBKO68UZEaL5DMLt+8k6AvxL5WMJSbq6T+f8PLxFcenI5bTDGc93HSbO939tMPfvX+H7//5d/juu7/D3f13eH75BafTM15efsFPP/1b3P+b9/jh//kDvv/7P+FumvDucMAuBHx3d8D5h/c0kRKbtK2fPcI8sSNjIdLmNPJ8u0y9kOre4d0dDg97nt6gsU1VZdSWmDwrEvgZAYkZpwvJI88xAsPwa6f62XV+PuHl5RPdI+YipLhins+YlxOW5aJusrWeYC3ZzddSsF8flYAq9xu1Nv0ZCwBU1VvTiL61AikZACJBbPUa7e522D/ucXi8w+6e+BSP+z3up50irxOPuu7u99jf3eNw+HWU86uBvxY2V6mk0DYyrAlQhdPg3FaxyYsrwX/Npc335jbfm4Tsw1XO5vd2MKBo128kfaVP5GRO3vPvpCAnAgmJ2Zhfsyn80jLGYAyeXLfGAakUPP/LC57+W0/49NeP+PjxL7icXxUSBADrPBuLtBeP1MjmzlWwQr7sqgN81UzHsoWrwsE63sgymJ1wTq6UGCwp4fh6pqD/8zNePrzg+HTE6eWsDNpvXT44tVg15oQcU9u4Obu9nyblFxTnkIsFbGGDF4fdsIXtNZvlccXeu6DX7iYTFqcaAvu7Hd4fDnh/OND43jAil4KfXl7w//npJ/zDv/0n/PjvfsKHf6KNf1koY/dMHLpljTsiyAiUulyoenTe4fCwx6f3D7ifJuyGgdod1mE3DLhLE/Jd3Yw0SlWblxbce3Om6yWIB7m/kfb5MFKSkdak5kPyjsk4n1QWhccnw/TtGx8AHbmS+xXySBuccdyrZlSBhavWdYYxtFnJiJVUcC44NHKi0blreQ9KLnDZIrui+hDCfyiloSSJdRWknVByRU5kjvX00xOePnzA6+tHtnid+Xm6VboLmqTTaNXKfV1O4ucTnHOYpgNPoJBYkyBv7w4HDF07TMYqDYyiYjLyB2yfAUEOgGbg0yNAAvmnXHC+zDg9HfH68VURvlIqhnFUwtk3n7cxeLff47t//j1++Jc/4Pu//j2en3/GPJ9wPr/il5//EdN4wOP/7Xu8/2ffYTcS8jaFgN0w4of7e9S/b0JD427E5fWC+TTryKnYGE+HSZ8F66xOLwlBsLdfFkI3UBVRA4DApnGiu5HWhDhxe/eGx39ZFswzobjWOpVVXtcL1nXRSQe5t/N8Ur0JassU7HFQJVmZZlLvg27EvtaqrTCzNIa/tU4dR8c9B/+HHXZ3O5pmmmiM2RiDlDMhoA973L074O7xDvv946+e49cDP7+Y8gBSIJRsloLvd9zvzJV6wSIxiFKRAK1Q1HpX1MhE3Su1ql+YzdrvLOxgNNMMca/jbx1vMMGxRGLZzDJXYdIncte7ZaVMhhrUww747nDAf/b+PX75z/+Mj//Nv8cvP/43cDw+Y15OeH39hBhXrOuFemNh1Oytf8FTIjKkWPDSedP4GjqxFzmHbfBvLHu6BxVAxbysOL+ccXo64fXTEeeXZo0pLYdvXS545Lwi58KwXdJpBOss9g+Ze/nNCWyqla9VVVnSKQQAe970DE6M0KjTVXQq8KOOa2xnGcaAw27Cu/0e398TxLUbBpLmvVzwDx8/4h//8hN++Q+/4OmnJxxPT9x/K/A+EOw1/jrs9aUlmxIgo5wJl0xozeunA56PJ3ycRjzkHaYh6HTDfhx0s6bktarWu2VL6hwTsjUwtsBWHmHliRaA7I5F1VEmOWREbjkvOElSx8mYD05JkQJ9DrvSeurfuHLuKm9+Htd1bgEfQBgooapVELUzQhixzgfdmMUiW4i81lu4bN+0IAgOJey7pqr7hXAdxIpZpheER1TmjNPzmchsp2ecTs+Y5xNyTgyX3qbeJglZLy9ba8W6zvo7hnHCfv+IEILuQ44hZ6rCQhPxkc9lG2Jrtu0OABtiIMBBvxTt86dMPBup/pc1Yn69KDS9zpSoSWLlbwz8ACGd+8c93v3de3z//b/Ap08/4nx+wfPzLzhfXvHzz/+Af/iH7/Cn/8efcHjcY/Qef354INTCOTzu91h/eIeSC8IYcHo64fxyUsM0H5wGeUlQJOEX4bNhDFpo9MXDukScn09Yl9gEcXJTsYzLiphvsyIHAHJijViWMyezbILDGgTS4xfL+lIy4rpgDTMCO+v5CxWkRDQXKfdmqNWz/5FA4lDFawFM0uXNeG3akzzvuB/VhXTgaaYxBOwHGm/ePxxweHf4asVv6peYYwD+9b/+1zdfvP9fXf/qX/2r3/y9/6md/9/yuQN/2+f/t3zuwN/2+f8tnzvwt33+Xzr3Xw38f6w/1h/rj/XH+mP9sf7TWrfRPv9Yf6w/1h/rj/XH+mP9/+X6I/D/sf5Yf6w/1h/rj/U3tP4I/H+sP9Yf64/1x/pj/Q2tPwL/H+uP9cf6Y/2x/lh/Q+uPwP/H+mP9sf5Yf6w/1t/Q+tVBz//URhuAP0Y7fuv6T+3cgb/t8/9bPnfgb/v8/5bPHfjbPv8vnftXFR7+9F/8FwDAeuhP+MuHT3j66QnnlzMpullsNPJFOUzsI0Vnu5enVa/1zrwDqt/f9LtVsWuNanMaVzYlWSMWdkxbLgsuLxekmDDuRzz+8Ijv//57fPfPvsP+fqe+Af/dH95/84X73/4f/69IMalD03yasS6R1Ma8wzCRc9h0t8P+ft/0pT05pYmEsYj4iMd5r82ukq1ZLE9ZkpjV3lLMamjTXwv5Oeccht2Au/ek43z/7g7jYVLVJxc8/jv7X3dr+tz6X/wv/zcYd6MqwaWYVXlNz29jwGI3hiy90YqIVsj1kGdFpklFm1qeH1nGoBO8wEbO1gVH+tTTQIZCnRJenFdcjjPOryRq9D//n/2Pvvn8/w//l/+3asBfXun5kuMVu2ARuJL7KddAzvlajMSHpikOtPNp0p1NqtVYlvw0b9UPC+v9yzuxnBeUnDFMpB9//909ht2AOEf89/7b/9k3n/v/+d/8Rd+1+TTj9HJSEZblTC6cLpCi4O5uR1bRbE6koiWb+2g2e8TmXNSQqLMkZtfPdSap47REleotmax+Aahzn/i1i8RtzQWwZN36X/4P//vffP7/u//T/x3TYSKd9uNFXf9OTydVB3UsNSuSxLKvtXNrDoOiTGfZsVLeA/OZeyv7gl439isAoGJeoiY5nxY8//KM19cPOJ9fUXKC8wGH/SN2+3v8V//Vf/nN5/6/+l//73H/3T0evn/Auz+/w/5hT8qQS8R8bjr8M4tRxYUsa+WYe9XVfon5lgjZOOf0uvngWPDGbbxLVK65k7qO84r5vLA98op1jqilwFhSufSscBnGgP/J//h/8M3nf767w8Nuh/O64h8/fMBf/s1f8eO/+xFPP37C8fmE46ejSkIDIFOcYYcwjCTe40lxMLDvQBgHWN9cJsWWXfaJz8lWy75PfjNR40GtlQypjiecz894ff3YeZKQn8Y47nF39x7/9X/9P/3iOX418EfWWl5TwryS+YgEXlLZM6q3LzfKOoPiHDxvwrZYBH4hbe0e8u7BkA27DwbQDZBemGK6F4UDheWXwgWHyMc3n2ZSrTsv7N+9VX761tVbK4pqnajKiezk/n5PBg1D29yvN0EyGSnqQVArUGyBKQWGBQdrKbDFAkGMjRyMTXDOIufCGuipSwCyHmNJWTdQNYWouPncZbOppfkwOFbUc2xB2Sd6mgRcW2HKBocuwGvw3wY3y7Kn+qO2k3bt3LmMbYkCjFGVMtk4m3d30Wt0yxIFurhG1FxoE5bE1RgARhX1el34WgHjths7JbTtPZF/o0tWUT7nJMbXRBLodp3ItrqIkdHgsc4FcSVPAbEJFTWzb12SbNI7RXavy2XBclmRU9l8bmFJ4v45cx5A/67zuehpXTkwyjUxhu55deXq2omKaNXEuLtE+oyooUul9+dWV87A5jCihijPrQ9NpZK8QUAGMewtYew2UZNg3x/r9boO/qUU1C7wibeBsRauWrWnLdZi1yXUxlhcLkdSUixJFU6/dZFqHAWnWshNMsdMXvRXQb/fh94YsHHmo+dWwDL1htQY+ff1CpG1VA78bV+gb6ob5VLrSAUSC/08FSXNJ4UU/2579u8nslpeYiRX0pVjXuICjO2ojbFw1iGEAdZ5WONI4pffR/EiGHajxgyKD16LpibRS3trCaS8KPtWiglhDZoUiMS5WG+L4m2MM8lpG4OUItb11x1Zvxr4E8tDntcVlxgR+Wb3vuKSjQFssNIH+mLIU7pUsiC0FsY2TXa6p00SU6sdeXG8hatNu37jTFUK0krBNQweafWaEc0nslEVV6O+Ev2WJdVH4eAHsIHHENRCkip9MicRqVXVm/edUxoHSVPfWjTSOZPxiGMZR3pPitpSXm+Wcil6M5asVsXNzOJWoxKxVAb4RRusnp+ekzVa6W2y87LduFsVSxk/Nv8tMsXtd0uiIcEOtdKzJFVUhxpAEx0A4ATLkc9AXCOG3W169TklxIWybXHNs6ahWZvAlcglUs+1S0ibTWdBAYCEzyAj/d/Nm79LAmzQ3pf+a2LFK6ZKl+NFXSBvOneVUyaDouVCFZZYCgPtGAWtKq7AZkMJetnez2udMLLstvLF7pzQgmePlEns4Gq+lKw/s3a/Q+RqAejec8sioyFP77wci7NahPTukZL0XjsP9pU9HXxF79O7+V4xoSnbPVBcCcW3AQBspQAoqNLurm7e83W5sNTvbYF/GAPZKXtxKKT7G9eEuLD73nkmGfUenWR/eWB7v+XdNtZQoWgrqrNwAIoxAGxLHGtFKZYRRXnK5HPQNPu7AlCOUX5nNPS+3brnB97LciVb7XWJXIWzYRpfZ/FjcY4QBjCaIUF/Ooi98KhGbD1SutkzrbjzFUWBZf/wwSsCnmJG9g4wht0sI0pOOAMqU22M+ao/y9cDf8nIpSKmhEUvQtYHrQo0lzK/EPRzJVcYS4HeOWwywcoZbTXt4ZXKVF8W2M0G12+Gkv277OGHzBVHQRgpIyu56AO6XJabN346j2YeYwxtCNYa0lDekSPSdBgRxkEDgrqPcQYrFMr2MlMmLdundZQFgzeXUixkTyzgF91a+ruljNg6q1V3Ng1Kr+U6Oaq/q+IFwN7Z5LYmFXktlYK+d+QDbxscb/EWqgMkccGmutdWQIfK1FphUTQAyMU3zuhG8PaZIA10PWZnGEL06pT1rSvxhqbHDt54rqo4ABv4XuFf3yyX6ZoBMFXbA/1mX64c3NTC02ITGPsKCGibm4dHGbg1tCYs5xnzkdy9bjp3rm7SGrFeqOLPXatDjhMAtelKVWQIDEn2AeytQKile9xV9Lzvv7kOEjSuiwKAbHMRKfjLvuADm6M4u/3Ab1jiA19SJoTLObY8toriSQXXP8d9YN9cIwBwb1EOPU/5Z2tg0P5bAv6bc3cUJIyl50gNzWqBgUEutxlzAWDTM8ewu9E9W2zOIxvhpJTYbXXrMinr2mVSjr+YAustanVU5AQPW6hQRKI9DgDqZ9pF/Bf9N2vZ9jkVOh4xdcr5ZrQHIB+amBJ7xHCLKTGqAbL6pqS0Bf8QAobdiHHHAX9HcSGMYZOQ9igOxYgCw+iYtRa5VN7/+zYqx0ib6HOs0XZfSgkpR/YokTj768Xeb3JxqLVizVkhj5Kz9qEyG/CUXFE9BQNwFWBrF7y7arWWimJk42vZcQ9LW4aE5ELJcUhbwRbKmDybG+SUEXLQ31VKVTe/9bLeDHnKstbAD0E3Ft/1FiUZMNcZZqXgXtmgpXQb3dW30eqCtrGAqX3mz/1frYLI43oT5BUOFVc4us5lva3ip/MmQx1xyqqZTJMAwDlL5y4PNB2Fbl7A2838c6v1/jqnxy99r2kviHyvQPrGcPC10pZwCGO4eQOQQCce9/J7N8mMaahIf659gnMdrLSlVXqr4r63L9yQ9v3X5w9jAPFvtwamgG17nba7jLXY3d1279NKCf66tPaeIEnXz/Amoa8WtRoYfvY/H/R5DwDQ509vgr4UAs4ynJ7fXEeAgn9d66bF5FwFBv8mQfutKwy0NbrgOYGj99tzsu2chR8J4es5K9cJ6ZcTn+7rV5wW+Sz9vlK1bdTvY9Y5VK6AxzJ2Nt4Zy3r57O/8LUveaz945W+J2ynZoXMfujNX+9LSrynMz89P6gohKea6IqlxHeqb69i3M8mcyiEn9+Y4bj3/xMlLZA6NushKm9E4OEd8Eu8CnKfnQK6ZC16LJIHw+5aPopNX+8j1MQvCAVASVCsZEcWVvjfvqBUQlwPW9YKcIlJOABJq/fVi9zcF/lIrlkjVfuagXxiOkItSa4WttJlV23o8/QssJ6YbQ6koXPXLarD/W+hfIS9xO3JMEklkeZhjRg1Fs19x5ovL2mDFb1zGNmKN55NwniwTNZPr+tCAZOIOQKXwZ4R4ZtqN/MxDKpV0q+YY+XAVEIc9qaSthXWVLH27Da+wdS+1YqidcOsyBnDeYhiD2rvGGvnYONMOV25T2PZcAWzQgHZdt0nddTD53Ab/pe/t20Ab1IDJPjne5lJW+F7Ihl+5byyf/wbSNaZd7w7RaNeiBcQ3ML5+P5QT0m9wn7s2xgIojYMBtI1iXSKA89bb/htWiuycKU6ajKRdH8cmqfnScX7mXhI/CNrL/tKS9y+73KokS/1sY/qWFrvxpbwhh90a+GW/sE56Swbee0Tn4AoRGwXivz7PzX1lxKLk7Tt/jcrBmu3l+ywysP2LtRbGb3vFOSbEefpdFb/l/c17Cl6yl0p1LySzTZCyBqZiQ1Ctpu1pPfL1pSAnbUBz9Y71+wu1lrrYwvtQyLUhY6a1iG5ZmZOZJZKD7DWHzTlPv99aeB+oHc18LrEQlu/ti8Hrd7lyO7SWzycp9L1cTBcwUiz29oVIw0wuD5cR1nnURA6WvxvqJ+QuY0nE8KWbL97wRW1jP1fJXj+8X8vIWnIAbSPIQ9BfeN1sugpJMquULExtJAhhPTt/W69TMn9jmo2u576LD14JPrDbh1ksZgF5IKF/R/cw098/U0WV/u/dS3b18BhjFGY2BmxF3Gfi5vclPcEzYztoH67Z5rrP3vfP/pu1myRkkxD+hqD/pc/uUaRq65uflY3hliV9aGvt198UOR+FfSWIy/F94Xd0wb5PFKyjDUGe+2ukoT931DYFo5tjKljy8lW05UtLGdRrY9Nft94E+rbebaoa6X/3JE66Blf3/zOVLp/O9vsM8SpccNTey1L1FUUaAKr8S7Koob3rtyJ9fRtG3jnrTKv4vdN73SM1PYpDBwVN9PqkpyXF9uqZRZsGulq1Mqomwa0nFIL2nGE3YtgtWNcB5cbg73wH85eKkoXUxm1PuR7WoEqx1/1842QQUiA8iz5J1GS5v+b9M8HnKP+u11T2v+66y37kGPmVY7t1z0+Z7MaXlJS30N9nIvYOmvj1fK7+ebtuT/WJiOwHFY0n1/+cfN2AULHSf6br3zUmEoYJwQ9Y1xk5J5Tf3ePnoL9w1p9T5geg6v8DreLRE1Por3IP3oASpW0GpMFpwwhvL0hJ9KBt2KLdkpt8zaattVK1vyYMV73Jb1kukEdyfxmtcwzp9OzubZWrfVyzTVwqPyRyNJRAMWO94s3moMSpXN48HKZSkqMtAfGmZrJlSyxu2/wE2aBWhqXenKWJA+ecBiuB5LaZedvorYMiH/11ov8nVOIa7u6vgU5/WAPYz1QOHUpSa+v16+Z6I8nH8miR80TA3FSr6Cvv9iI6bzfXfLPZdSiHkJSkMlESo/zubvRT1pfuo7xrMv4j8CQlIvGmcxc4NwljO1+9e5uEm/gfPQ/E2rebdu3eD0n6+n1DN/2UUbmdVfjdls3OOYcSinqXl7I2ElsGsnXM98Hmnbh1bY7X8kZfqh57H/TlHORdlZHC6+sgLT1juvZfAY/9Gr22ADbFj1562yUczsLJHpMKwhjYw31EXG5877txVHmudIQ4ZcAYJaaVbo8nfpfR4wMAU8qblsB1cr6Z7urOt5ZC7aI+OeIqWH+2+0yaBmlIgJATv3XFnFFqxZoSUsybvcZYGtG13V5luRVF1b7j67flLAHYEJXpnUXb41OH6NaG4MnSOPK5EUlr4Ty1HJxz1PrCr8e7r1f8pdAFSEn7R1Xgnn50rDshIfgkYwCsqDUAvqLWNh5myxaKcQAFf+5XKsTTBcaSS7toXaYvF2wTNDJV/DKO5YfbCF5S8fcPmA8yqicPPz28/QPd9/zlZddNoNDDW0u76VngtNw2WYX+u1XL25cHaNmlfI98XhjDm43jty4i9XkNTK46hr2sjqcI6aQlZlcIBYBau03+C+saJqWkL2/6ypzWoHb3epNolcIjSPQZQjq9vobfcv4UgImIBvQbFrc7hNXdoQNv59e78+srBOc2Vb6eRzfD3ZjieDMumZJBTgIXCsy7ks4Ej9yVdFvVo5oSAvN3gUzvrd4HSgStVIrds69JGsDo4Ladp/t5Xx0Fo6Q1zCuhZ7klSHLdS6F/r5UTThDEmaNVOPo/xuqTHmst4LaBR9oWfZIvzGzDqBP0/LctMQtoQm27SrZf0vsmZLVdg02LlJMR66zqRrwZq/2NyzKaIecohDlKtBrPSq6HGQyPzzadDr0WKSP70sYiu/u8gci5dbI5Z3D12xd88ne97u286fcLanL7CPccIwX+lVvb3XUUhA5oySAlvkRy1nFu57Tt8bnHUNA8ed8l0NdaGnrHSVC/r0ii1McBKSC8I5IhXYdff++/PsdfCpYYdaYwJyL00c3fBqGSKwDu/1gLIhnQ7G3mjS4Hp0ImAsHqg8DZr/ToCwf9nLMG/XyVPV5XifJvtYIroIicRuig/DcuIfTlmJRl2mf67cV4Ww32Qi7XG758ry0GCdANoU9y+sRGfx+w+fqbxIBwxc2md2uvi4R6GhTtPADQ9ZBNuJ+rpaKlUhaHbaD/nLAP/buIOzntbQO0YSRjgJhQ63aDkxe8IG/gVQ/ADpbH+mhdIyXfsmqtNIaT7RuyoeWgLGJGPYS5/QwBI3gDKLlVJaYA8ox0weFaSXtTcRgD49umlmS2nwmtuWu/ARZxWXHLSjy6tS6RElJ+5wy6BLsL4G/QgKt3RCp+Y/gZZyyzdMiBVOc9MiJjchR4vCbDJZNgSbaOzzVrMSBJb1wThnzbvffebaqu6yRCkv2M/Ca56zf7Uqryc7Rw6jZ02ScocDo4L5yYDvIGQ8OSRPWJJR+joK/GQBGYcGPes9HO4LYK+Bxrrcr/sL4bX7zaYzbPq3vbCpa9UNAy59ymH65kxm7PFZEb/mBCIW0B8tuW8a3vPACc1wW5VKyXlRBnCKfJkYgXnxeNfDqe+rCa+ALQIs461yYfptCNLjfoX94lLf66CQn6vgoEAAUqbCW6Cf05C+cAoFHDX1tfDfzzZn4/aRDuM45aaxt7yu2kcjJbcQu+wX6gvvHAP2+LQcmtX1RyJpU6JhSl2IJ2n/EIVGK4+syBoE7Lm2DlRCHnfHOvTzYk+tNVOlZecAnsRm+29GdEpdDzCyJB3wdP1VgmcqSVB7dykvMZFroQPIw1bVqCv01eILk+OTd0RDLrW1aYaJZZCUwc/IllLJs096GcA4LTF3JT/VyN+EilJ/dNpwb4WaER0QS7JmTvNvCWVh9CaOO5Z3oJmqgQODCnNW2bxt+wpLKQJEvhXs6wRYFLvlc3QdPBeVcVPP0/V2/ZAIZuou2qXz3XThGwX4Q6ed2Y5fwk+BhrgCx6Cjeduqqx5dgqHnl/r98l+b1yTeR7+oJANmw9vg7mNNWgFgPDHA1T2vnLdZTP94NvgbVW5Ejjr6UApm8R8j3r945vWX4MiDNVfJlRTql0RV2w16poehRyn3nahMc2Sy48GdE/C1n708YEgMfZ+jG265E41IpkDGyu/HNbpjtAAjzDNNxObNQEZvtcS+Xpg0Pqvk/WdWvOuO1INsABuVRkOVaPTVItZGF9TtBQMxX38hWA1/c+JSZyr0mvty3bFsK3rJQLlkTaFXFZdTSQkmF6JsIQWD8mbGb0JR8WxMm5dk9kOkPiQJ/QlOCwLpH+m5ECQX/lfZPnT7k8eds+cc4jhBHOfV2/4zcp9y2izpTaLKME1h6Oll4vAM2EresfbqMQXb/koUKRarZuL3TaEovk5HtITRTxZOxmMyNceIO8YRlD85IkH9w2r1okAIpKlO166/3PN3h3g0p0M6/GUnC2ycG5TgGxe3FzzrDWUM9JGMzOwZiiKoHy0ClMy/2pWzeAgdXfHD+kAFCy0YpeEI3rGfa+YtBNs25lPAXxCTz+0ljE9HvWJcLzMycXtEd/RM75mvwmQhp6PF0l+a2LEhDasGutVElZbAKbwLwAVSkCa+tkSW7HL0lPzhY2ZoWsZfPQaoEJqZIAyrVraEebDpF3oykCQn/m1hYHAOULCMyv14SDrpERx47UKu0Z+u9t8qdVDF8TeW/pmOn5J9Efs33Hr97b/ryEfEqf83mNgVs3f2OMchxEtU0SIRlf7pf1RACV4C/vhCTd8g7YbDSgqtDVZxj/JbWkTxPGYgDv5PVrrZdr0iTvs7dOdBiLTTWqapWMcAkfqecyaJuv26dNFWIcvyKcrEvRQs8A7S8iACXXzOgPdVwKKyih0wdd4PTCcubS+nLeYl1uI/U6a/W91/eA1WrXedVjIvXCuIH6bYfGGUNSzsNuYCGfQVVPe/a/xFUX/AbpFZVKeXdyEh0Xx/sIKx1aQhtCGOld+grMD/yGwJ/7LIMDfkltpMN5pw93zywGiIJBwj4GJjIRrBQKYD1BRSEv03rFml0XRQCMVNpcLWTWjyfN8l5op/XKbu3zyJLglVi20hhoRmZ53pXkUVsV31d68uI6Zj5LRQwAxjU52Voqiqdz1Qen80FwlSAjFzJydK0dkrN+Zr9RyFRDWhPq/rYAMEwjKXhxX6tWqD696Bo4b+G830DuPd9Ak7a6Tb5Eu1peAoXM+FnyQ1A/Ark+gobU2tod4m1QS3sW5VoAPH53I7sXVWaX0+Y+CklHXki5r28CJOtcyLOQ+VmVxEESH5kAkWuY1oTlsujv3WyychycjPWbvsC9JW9RilsWPfNJxVkAdBMLneZCJvIXsFL1tTb9denZCoSpymN8X1ubyGx073vIvE8aVLY0b991gsaZ1FS3st+39vmFH5I6yWLZ/GV8WapLY0xj/3rAWqeVsazCKJkkPHI96Pybr0f/RwnB3TkI0VfPHVBis20g4O9axjaRLv09VuS6aW5eCq0aK8oGpu7geDSyniIT3R4hcH8YBx6LvvLu2Aje0DlKgQAQKlVrVfn4nGjPAyi5vnmaxzQeiVTkbZY/M8oQsc4W1rqN7sGwGzBOg7azRxZ5U80X7/X9uFau3aCk/HylNakfwjpHJJv0Z/o2CCHLno4nbEe8P7d+k3KfVPhSiSt8+xmop3+h5d8ExhPtaBLiiLDOUBALMhLY9TwUJixvFdRMay/EJZKOurDiO/JM67//usjEr56/zjMnrrrpYjtv243ejSpw83bTKg2CdVZfaAoKW16CL3Q7egjxmiTYE4RyTFiXuKlqGkmEphpEdAmHbz930XsHZ9t9P19aNr7jbBhrt4ytuuVk9MdpnG3Vvu8+g891yG3KQfu6pZ/wAFJMDMdFeuElMOvGJRXV7T1+Siyy3reSM+JK90bQiFJc17vDNjERgmGtGjj69leaBjU/0mS2Q7pEOvd605RkSdtoxqiYlqAi1wzgb1klFe1N6saEt629HBOMi9rSCtOAUAK9c90cuBBYJXA2JIh+nwu0oQlqQ4pxDeru2eP9hI+xRCYjDxC3efdF/vaW1UyC6E9U2dbfsI9YIgCLOYvhJLFxFVoLEuhJpB1XwFALNHeVv6xrJACmZ9mTil2xvy8F0P6yIz16AAjcXgUoOSAkbNWx6eW8YJlXLsJYRTLHDXpp0Iof50gLZXdHbQsYkbwNzfBJkkhuAUjSXHLFOq+6Dy7zCuss0sqIVM03P/+D9/AyVSOFJyM96zqTWA4n8M56WEfJyDjuuLClpMN6egbG3YAwhEb+82+JsG/ao5XamCKgJXFuvay4vJ7pQLsC02evxYEP/qto328Y52M4PRetuK57ltdrk6F2QVeCWebRnOsRISWtlKrBRV3LXG26AZxgxHnFOi8KabdfKv1f2bi+fKxfW5lHOjKfswukBjdMFPBFnnEcAgI/MNYYOsZakbuqy1mDXEgYIsaEWhMqEzfk2qhugLWbjPf62kogWc4LEU4Y+k4x6QNBY10Zcb6N4HVNXJM5ea3OuVqXTS4weaU/1l7Duydpwhjt70t16LqKv0/irjc9CT5xiVo5ZCZjSWtFVskVCbf1eSWA9y0e+UwJQgDg5Xn1Tcyod5KUZDkuUcehAB6XvCwM3XGA20x4NGStD4imNp1vCfo9AlY42cg39rcBdGO7LTgr+pUqgNiqCkviNiIoojKlrHC5qdr5eRAeynUfU4NCp02xYcV3rT3REpF71e5bmy66NeGPa0Sc26ab4pX7nKB5kJGuRvYcubobWbLVeqtohyRkKfYz4q1q39yDmGHddtIHoF5vNQawrRASGW+goUNmvfH+M3Su+2/32YAgNAkzZmp7lKoqj8v5gmW9IMYFMS5IcYGxkhgzYmQsLPejx7gnkbDdgDoSgkLPUbuGw25Qd0tJwOMScX45k3LdSoFfgmOJGYC5udUx8iRTjokCLbt8vr4+4fX1IxshcRvVODgfEMKIaTrgsDyopL0xBmUvrciW1BnbnpUweHjr4KxFqVVjR60VqWRtswzToOdN1+KE+eQaOtPtHzCtHful9Ruh/h665i8Ys6m+WzLQyQxy/+FLDMtfg+L1ZXIWJTQWPLUZCnKiare3g9Rjzq1SkZt/a+AntIF7vM6R1e2OdJiHid35xgH7YcAYAo3kAKioyFIh8820xiDm3BIDPjYHhxoqwhRQNelpesyfC3wlF8ocrdGssNYIRN74UkaylsYZh9sgL+lZ8S/eBCAJOHJdrTObOW653D2xSyZDNrC5vYJ2c1ex1avAX+qmp2wM/U6zH7X9odeJ/+7SW07Jb11aqXZeB5mV4YTbIEFKqhJrLW/URb9fkJmVqyGADDV64Ssh57QiriFEgq6EwSNMg/5doMySaNMFb/TUjsuIMd4c+HRypL8PUQizEbkkPgeRbw4U/D3Z44bBawLQJ7CSoPRjuoKcyD3tdRF67kM/YhjXtHku2nEWvSa/h9nd+rpdq8caTXbIu8Fo9SaeEL1jpxQFYfBdNSdtH+IN9IgKwEG9UJJMUsmREaas1b8G+ivtEussgvG6763zbdyWPsmQ508STZELlzYv+nc3ZcS0YlnOWJYLluWMGBc6NtvD9h7DMGIaD3DO836eN2iKOE4OU6BEajdiDAGeA+TRzfRe7UeMF0oQmqdE1sTvluWZGBfXhPk84/R8wuvzE15ePuDl5RfMlyNSjlrUhjBgGCZM0wGXyxHzfMI6f48cs1qHh7Fyu7q39jYwQ4CzFl7eERhYY5BrgctWr538zDgNtOc52xwUGR0AgGTMm2fqs+f4tYsQudeXuarUjZhvdDFbEs4GruqFUzi1DQPJv4ZR2JDbURh6kDomaSeQI0zunFKzgkxv9bt1bIYhtVq7iuIbV+beDsB9aa5sRSgjDB77YcA0BHhLlVuuBbkjYvXXMuZEAhG56AzqtelLD3XGsiJzi0Wuu+DJtUIrJP357pxrhb6otyypxvWalquWQsn6cMsG4DNZB3tPIy7BWwQOkGUsiB0bmg63KpyNtO0NSqukX6IKJ9eiVnASEjYPu1TpdSi41Z40LhHLvCozXBMWfpmHiSqRge2Yw+C591+wXBZlIa8AwHr363pBShHzfEJKqyZFzjmM4x7juMcwTBimbbUz7kdMdzuyfhZkxBh2opwBnDkoSo+zIOfbxHv4ZPWvAttW0DOQ4oqUIycAGbWWVs1Zx65lA2+IO7UiFRRA3uP+fglXR5I7eaYF6r1GNYQh33NbKit2olZkYxVluGWJJbHen44n4rq+tYxxKeolwb+vWKego1+aAPTIzpUHe47U15WRVmstqq00TmvEfMq94dYARCoMlZLsfi7+1kUkTu6vwxNysRpt+362jVoras3IOSLGGSlFihe1wBqLMExArfC+6ck3Y52iAlRxTTB25Y+sKLuK0LHVdcrg/9vef2xJkiRZouBlIFhVDbh7RIKq6u73Nm/OLPv/P6F3s5k50/0qK0E4MDczBQIZzYKIWEQ9gIdrzmLmlfM5URkVDkxFVISZ6NIF1hKMzu+FfJ5bMzqkWRVEde4nDMMJw3DEOJ753V2L6hh9fgapGFhROltaVE25QQLpeYk+kPyuDLBM1tNKwfA+bqARVILVBrDr66i1RpVEGbUhGK+wHJYNQfDX1tcPfg65kVQ+ian1fu205SXOWkZjYKxaq/bNHEMibbddS3ai4v+NmwqGrmXVtq/5z9wxmZXNHWMEmHCDsD5M/8ysU+BeYD2QjbgzWQ2j1sLEhUBmR5xomFLKsE2IcZPnvJKdJOVLFdcEPbeEFcpf1kREqe5yRW702vFsJFJZ9XBjxweweZFWWVue5+aBUBApMIwxlNEtM3uGeIuqIGVAWaCtLSprURXX92ReHEKImPqJO6vNoc9cCCkAxTBIW3PF5ZC5/raY0EbzBlTkMc23Lske9wupKFKMZGFsqQNp9y2aXYNmV6NsyqsOfJ4WiuVsKgw8k5v7Cc4tGMczLucXTDNtIEopFEWF3e4exli07Q77hx12D3s0+4ajpRu0+wZFRZulwOfjZVo3qWnJvgvye279/rW55qtsO3zvKQpUtPg0AnBIKVy9K0oZVGWNoiQYtOl2uXDZblrrphjyIQFGQLaJl5ln4UNGTL6s6WQTRlA3H/oA1m48JjpMv/DhELRqtcsW4qfOVt5i8qUNjQe7pkZlLawxGfFbQsDkCE6ehxkpLTxaCKzsiPl51kwgNtZeS3g3m7wUpgW/d7es3JFK07WZPUsXPJwHDKcBi5BQmbxY2BK+rOCDg9HCWeJnJnooRU1CVTVQap1tC4t+Hmb+MzTK+zICXWS/AK6QuM3HhFg5/5Is+vcsrQDnA51704J5nuH9wtfA34c2sMaiKGuUZc2IVwFrSyjwOGKZMZ4HnF+qTE6WkUVKKZN7HRcrRmsk0PgosTTVbJ/7lJAM86PqAk1qAOCKMBuCjJR++9q/evCPlwnjecB0GXPMrZtd1rjKBqyNzuQelKtH9nbTFkcpWxZ5pmu382LuLhE31pXqOtiGcgLSz+bhShOBxi0eOiZi3keCBoko9U8QncI1JEufhWaO80IbtwuBDjK/Yf3y5xGi1jbKUjY8eaDLusxdheeKf7yMmC5jHmfkueUGTaACqoDSyBWzdBOymd665AGlDXTbTccruHW7gW/njVVTotm32N13MEajrGtYYwjKihGz95gSFZb9a4/xMq5VOm/+mkmAZV0iGQPIiIF9E6gDiXkzoD+6hQzpubxlTcNEBKLAkkkrZKQG7b5Fe2jQ7Fu0+xZVW2U2bYwJjQ/wdzsMhwH9aw9tNMbLCJyAeR5w6V/R969wC8342/aAqmqhtUF71+H+xwfcv7tHd9+h2TUMF9JGPvUT/MAcgs3sWSxDdSZ6hQzFf+vKM924VdiEK3if2OuMCEUP5xbEuMA7stFNKWGeB1RlzcRYRkU24U7b4iQEzyiIz3+/MQZaiRPaF98jFyRbZO0aNr/94Jd4b8VEPaV1RnfKurySb8kIS9AppZmU7D3MwtbDsYA1Gru6Rl0UdPjHiNE5HIeB3BZjxDzM6I89pstIxN1Nc/ClEkauN0aV2fN033RGHm5Z3nmUm3Q3YepP/YT+tcfp8wmnzyeMlzFr52UZW6CqWshIiMh9GlrP+XulSFsLo+m7DSHQGIwP23mcUVyKlfzLvgRlXaGQUBpG1wTNVUZ/gQ6vKaLfuhYfCOI/9Zj6iQsWMsepqoY+t7Go6w5tu0fTHIhRr+g5EcSrrEle5xeP8TIhJcA3hAqlmHIDCQAujw2pmbTGoDDmar/MjaUOsNYgcfJowcWEsZ7QNWf/eah/6if0pwH9acB4GTEPc66EAvuBg5mYZNpD8r1oDLRJUFnbSgSg7dxPs+/xGvDBJj6aukKliAC2XVorBF9kmG9rdBFCyNBQjJG6bGGbtvNND4FbXJauCBRHh57EdhJJZy5s3sRExuUmikcdL2OOShWZVmT5WXtosbvfobtrc3b6Ms3ojwPG84B5nFkutS7qvOmLLesiV/yeixwxX0kpZenLLcuWlHgYNyIhQRQA5I1b2OpfSrRsWaAbZsQYUVQlmrJEwwRIozUmR3Pvy8sZn3/6jNPnE5ZxQVFagra7GvWuYZ1/kUcsYl7zJYHu5/nf4O/otnswnIbsUCabDx341OnL9+UXR898sHztXKw0PBZi05nh2OP0TJuiczOG4Yx5HrhToO+xLBvsH/e4f3ePu3d3aPZNfgemfsLcTzi/XDCeh8wMFymrFFzba7/14M+JbDEhppAP/eBdhmwlhxygLktrm3PKl2VGCA4hOCxOofBLlheagrgymcMSYh5VbQ9/6Qip8ydTEq1tRsZC9Ay5yvO4jht+qRD4ljWPC+v16eCVIpZQnpo02Xyw+pnMXqaeDF+8W8cRy7gQcS0BTV3hrgHaqkRTVvSdTRMu04TE+4V00nTg0H2x5YpqShz3SoJNgEf2/M+opNWo2uqma/cLdfDSYEgj0r/2OD4d8fL+GcdPR0zTAOcWICVoc51SarRFVbWA0gjB5Y4/xghrCtR1h7Jq2NkuYHb0fBlj84gkE3/53Wt2AS3azC8ydkWKMw+BnyMf3Jrh8I3rdejRv14wXUYE56GVQVnW6Lp71HWHGCOMKdB1B3TdPbrDLheDmvkp27FOWRXQlgqc8TJmaajIUkOIuQCQULSmrrCra3RVhVI4BzFimGc8p4RRENEtuitk42IzG/iV9Ts6/pGMCvjDhny40PzQlkLCqDKr+8tcem00d0o1qq7OG5lU6sFHpOgQNhWbNgZls9GDb6wK/eI4dhR505ODQP7e4Dz8THyAaZhQ9r+dT/xra7qMcNMCbU3u3l1VwHLin1U2E85sYaGVIphwWuAWepH7I1WO5+czTk8nTMOElCLafYf7H+9JwsJsaPG+lyLjSyvgLOPaaDgVF1wy753HGZ4Z784YeH97SldkkxCEa/JdUZWoWjIUmvqJfm0T2wyPlV9hDZpdg/2hw15rtFUJHyJO44jxPOLlwys+/J8f8PTTByzzhLrZ4f7dAx7/+Ihm33LWNcv+NioDbQysXdUL4goGrLyJLxnJ37LmfkKMNFek66VipKxLKE0FWrjQSydkNkG1qq5GxVyW/eMeSmtGcSZcLi94ff2IlGJmP5dlnaVPUviUHIXcH3sMpwH96wU9HwrLtGwQHw5SMtdugtKN37L8QjNu78W9ziEET1DkBlclWJW62xAcYqTOvqoMHeC84btlQkKELQsivrXUDREpNcEtHkVRwDkL73muGwMlJKiwsuc56pXmxzOjDGtHZrQFmGdgrL656xeEM/iYg6rqrkZ332F316Fpa9q7YoSrPb1ri8fUR9JdT0ve0OuuBgB09x2M1thVNQ5NAx8DHL8vUz+jP14y6rWOsdZYbGNXdFSebep4v7D25rl/eWvHv9D+XrUVFwAx7y3DscdwGjHPI5ZlwjT1cMtEP1vuuyE9uXTFgj4BVIhqpVHVHXa7e9QdFSduEbLrCtvLyNDy+0DvX4X2roPJSpgle6TkkRHzT9JXbGt/bZ2HCeOFrqmsK1RtQ8+uLZmrEFCWDRUvdYlm3+SxHyWZ2kyGFNlfSgnDmZo5aQbHS4VumFF1NaG2ig7+oiowdzWCNFh1jbYs0WgKZDqNI8bTiMvxwgjRkBEiADlA7rfW1+V87CAmtoUpJYbnm0w42jq7ESt9w8zlzbqsSzQHqphtaTMTeZnEHIM6RjFDMGx+UNblmgU/EQw0XtQVI9bNLnc4mmExgqnZctGHvIl+6xrOVPWJlKQoLfxSZk1/URf5i40hIiTSl45nhukZ5l/GBaenE/7xt//Fm37C4+MfofX/hsPjHlrTBqGtRkrUbfrFYbxMudDRRqPdN9g1ezS7enWkSynPekMILEOiYsXa2+HOTEzcGHkIy7eoCz6Q1whkr1aZYWDNs7nQPL5qKhzeHFA/POCx28GFgJe+xzzO+PyPz/jr//qf+Omn/wXvF+x2D3Duv2ZSWHAexXn8wjeBXhSZ4woRMLOetUiffp5u9nvXPE0wtli95A3xSBZ+Dt1MulqlVIYghdTVseFU3dVouwbaGkI3Xi94/fQGbbtHWTYYxzN3uXRoWlugu9uhPbTo7rsc/xwcPUNlLTC4JijZGJR1dTVa40cid+i3rK0jm5iWUAdusCXSee8ySTElOqChNGL08H7GMk9U0IA+ry0tukOLetdAaZVnuuKSp8YNURcJSBFK2Zw8lkCKHir2I/8cx9ccgQKwigrofyaZbziP2WtACkcikvFhJHN6ft/ncSFkcZw3jRIVNeNlApTC3ds7KKXQVRXu2haTW/DSD1hCyLkISIQEEhwcsx7cCHeA0ZKiKvMBnwnXm+8/OA9344x/HmdUbbWSeRU9/7a0qLj4MYXBeB6htcGkDZyb8/NAxZ8huJvZ7oIO0vUVqNsa7R2NyBBTvm+2LHLHLwfptuAhrk2CrvTK/9nwRaT7DTdGEgNU+ADga139JZQyyDI+beG9g15UHrUpRUTjorSMWJDBWdVUmEd6zpdpwXAe4SaXEfTurkWzbzOSK1L2l7bC06FFd9dht2/RVRVm79GPE9zicH4+4/x8Rv/a5+araum+fa3Z+frB79k9jaV5orG0hUHd1TCF5Qd8PfQBZIZxDDGTXoqqQNPRnHecZoQLVZCnzyecXy7EhNYa3aFFd7/j6jrlrpHywSmBTOa7IaxIgKzVAAe5e15u1LIvI7G6y5hgrclQ/8wvd/opZQ29mN3ITGwN0qH/f7j0eH5+j48f/8IzqAVNs8f9jw946yhjwFqSdLnZ4fx6wenTMZtiaK0w7Bp6WO53V2TA4TxkIpoUG0a+sxsPPlFcSFGTUiI3Qd5cFtbSvnx4weWFupV5nOD9kjsxaytMl3doDy2C8yiNwb5p4LxHaS3c7HD6fMLHj/+Bn376n1iWEYfD21xgjHzgb12+6m4dA4h5kqxtWIbwRG7P5XZIiHCTycoIN1EBJs8fVfwt6rbOs/hmR5+t2TXoGoLrfF1jGRcc3hywu99jt3vAbnfPZiAeTbNH0+xxeHPA2395i3d/fos/3t/jrm0BANN/W3CZZpynCf1IHYOMRow1hC6dBgTnMRX8eVOC/yeY/Vtei7VFJk3RIb/mACilURQ0gy+Kkmf7I9wyIyZ6zhc3wTnanGxJPAlxG4s+YBlnzHYlMgHyHidGrCYEbzK8T78eGEkgQpQHoPX1fPNWxOP4dMxEsqLaKhzo+mfvoKCyXHM75w4+YB5nDKfhasOvuxpPPzziXx8fSSadABc8xoWQoPE0YBpmHhUVuAqw4u5esieU0QwhrwlwV9bp/wSp9/Lao2qqLIujIpuehaop8fiHR/SnHpeXC9z8FjHEnIIqSIfM86umRrtvGd2hPfjLJnCZFnjx+mCVFiX2rcmXYh0dHM3fxQQrOJ/H0VM/ZU+XlNJXo2l/bSlD51zd1VeOsJYtdWUf0lrBVgW6uy4TcLv7DofHPQ6PBzzudugqQjT+8vSE4CP64wXLuOD4dAQAdHcdj+noe56HGZ4bRRopmFzslQ3xfOquRvABl5cLXj++4vx8xjSMMMZin/Zo9w2q5rcb3d/V8fuNe1iOITUa87Qg9RN90c5jHpesx2VuFqqmgl88iqrAQ7pHVRT5AR7OA57fv+DDXz7g5f0LpqmHMQaHh3u8/Zd3efOXeXE2NWE9rxDo5KEU8xqA9aK8+YsM6JY184xaG02Fx+xwfrng+HTEeCGNp+izq7ZCs2+ygUe9azKZUSkF52aMwwl9/4oYI8qqxuvrRxw//YjzywX7xwOKOmBiU57oI+ZpwXA5w7kZCgrTRLDO+flMsjYuOogLwMUNb9Sybk7nqwp2rVtyRy1jFccM3NPnE55/esbr588Y+iOmuYdzS3Z2bNs92nYPNy2IXzipRf5e3LRgmnoMwwnzPMCYAsNwwvn0TFVs1UIpsX51MJa667qrsXvY4fDmgP0DzdnyoW/W1K9bQ4poFk/d7LIssLbInb9SClVboT0Q+a49NHkcULUVfe/WoDQGRis4n1CUFofHPd7++Q2G039B8A5FUcG5GW17wOPDH9Ddd2j3Lf54f4//8vYt7toWWiksng6Ifp5xHAe89AOe9y3Gy0iksH5CYnKYpLNphlxvWTFQt1lEkgo5vzCU77nzrbP8EGBjKz4o/eLRny/k+KbIsCVLFTc6d1vQd+PmBdMwo6xnFEUNrS+MLsZ8iIRgr/gEhG6RsoBGD9dZGEIyvbXoG08DIn+XssTCVwpsmct6JvcJ18XN9HuOn19xubxkVLK77/Dhz2/w712HJQT4EPDT6xEvH17w8uEFx6cT3LxwYVTT4WJWxzqzeY7nYUZwIRfFsoSDQ3yfG5udidnsw4xmV2f5arNvsrfF+fWCxz88UhPIh7d0oNLJRh9gmQxLrno+B9w0+wbdoYM2CufnCD9TB5wSNUqiyRe0V9DmrSeCdHbL7DBdRowXGoGJdbNwP751aU1denegkULVVljuqAHUhhrT3cOegndSQsVIX71vcNh1eLff48e7O7zd71FZi/M0IsSI8+cTALIanqYeMdC71N2Rraoti6zmIE7FJcP323AsijA2GM4DpmHENF6wuBllQd1+UZVoD79t1frVg38Zl+w2FcV1iyGmNQEvYDyP6PsjstTBWhQFzbbqfcMvooHVGrOnyM/+tcfrp1e8vH/B589/54O/gHMLWx2yProq8pdMXwyjCl7m4JHnXmrlNChHsiGtkW7UcQPIkD5AhYV0VeNlwtgPGMcL5nlACB5V1WB/eUMPRtxn2MqAdbvMcpXZ5DCcMQxHDCci9AznAZ1qobWimfjjnkg+fOA6NyEtif/dMaqhmXi1Sk3kxbA3Gvdsl0CJ0cdsjQzQV7HletDGVMAw8TKqAMMzvu6+Q3e/w27foi1LaIW88QHgkUSxHlKJOjhjC9R1i/auoxGLC7zhUfXvZofhOFz5GFRMcILedGk3KjpIhkSbZ/AO2tALZ22JqqFne7yMmbQjVf8yznmOHe4i2kCHhzIazaHF3bt7PL728O7fYGyBcbzA2gIFE77mccbkHMZlIR+NEDB7j9k59POMyzzhMs20ybGr29ZSWyxUbyX20VeQWBP9JbnWZH1+s6NrFLlVURVASpj6if8sWbYiJTTNDu1uj3rX5HsjGe5FRRtnKU6Yc4sZA3dsQvIzKIuK+CzBYZ5HPhCpGBBSH5kIldno6Guzzt+6fv6LM8FN5GbBx3wIx5gwnGh2258GDMce/WkgPs/xEy79KwB6P14/PuLp75/xl32LyzRh9h5Pn17w+uEl84DGywitNdy0rHNtJrhqY7LEVt5H7/zajOXPGnIHfstyE/lXENOeLGBlFp8S7YNCmBVLZqUUppI+e2Q0TFtDstcDQfq0B8ZMPCzrilFEjRgTG/5MmOeRnPBaelaK0ubzhp5BlRvLxHJrKbacmzLX5GsJdb+2rGU0m8nXkhUDAGVDBN+iKjKforQkVW6rEl1VYV83ODQ0l/chYJgXnMeRCfI8BvIzodVuyaZglmWYMQS4ucRSlesIh5u8eZgxDJ/h3IRlIXmw9wvvgcQXEy7Kb17j126Cd2tCV9bFZnMVYv26xWFZRgAk1bCmgLFMyuBZTcMvfFOWbApEkM1wHNBfXtH3Rz74qYK9vNxR93PXZmtW0VJTEaGAJeWQGmMMsPmiyc85MsP9NqgbuHYXDC7AJ6rqhTBHnXULYyxtboeWuv62ytW4Zz6D8wsxjiEkFIIt3TLTQzsTz8GWRAgTsla7b3B+aTENU/b+F20zfS4P5xQdAunavljxfO6WJTHD+YUzGkkMQyKFLZV1ifZAxUrddpjHieZ9wcPYArvDHTHU397hzX6Fvpz38Pxd2sKgqhpUVQvvF9iiRFFWaBrSsh/eHFAydCV8h8D+9tKN2NJeRRMLGrRNu/rWJezwEAKCImJbjOLbXxLKFVNmPIvUr7tr0d3RqEobg6osUFmLpq6QHhL7bRP/Iyaah1JXGzD3E14/vuLvj0/wIfxM8z0uC5ZxJl8N7jClIJrHeU0UYzc8rW5DO4jYyfGvnMRXqCr7q4u5UFEWuesz1hBUm7X3tBeUFaEDdVtnRztR9sSY0OzqzMVZRtoQrSmw8CZO34VFVTZ8SNAIKbPFA+U0FEVJyEJDP4NQl9uLX+H1hEDQ66AHeO/zeyc8iIUPnekyYjiPROjtjxjGM/r+yIeQxenzCcenI/YfdlkVdfx0xOW1p+90WjD2A0JwmIYm752i5292NSITwUSqG0KgcQnLobfBLvN428E/DaQemfifeZjXIDZGNxw/f46zQKZ+wuXlQl3qtABKoeT3Yf+wQ71rssxY5IaUoOeuyHlEEg35PdNa5wCujNxuUGWxPhZkSGD5oihz4/mty3OugijN8sgr28irvAfFEDHxaGD2NRQUmrJCiAmTcxiWBU/nMz6faBY/nAbM80wjL1ugKMrsa2EKiwrYWJqv0L94m0gyn/cLlplIliF6FAUVUVAkEd/d7X7zGn/3W6G1RlTx6v+HBeDpwavrlkwZ+OZY3pB3D3vsH/doDy3qqsxa93mYMV7oJRnGM8bhjHG6wBhSBpzPr9gfD1jeEkmGYEGSa2gm2AQfYdlkQwwtcsaxJ1KZWxyg5isY8FuXkC6U4ZQq9uCOsclkDCF11V19ZVyjlMpqAHmYhYkonymmwBadTERsSmKHsmENVXA7mmExCTIXIz5czdc8Q6SGu1NtrmNzv+m6sz6cSYzB5Oo3OOJd1F29MtFnh3mo+FojrLXo7jvsH/fYv9njUDcUeRkTlrCmO5Y12Xc2zQ7OTVddXNmUNDPvajLu4QNdJI4i95GNXiyDyXY05s3klkVxoTYXEiQxU/DeZFMfY1ImWYmqRGaAjaeNRytFUsaSrJ1TiCzxXPJMc5knWGvhFo/LywXP//iMlBLqts4QX0rsIZ+NnXwuhGSjXiYhygbqmG987uVwM1YjBI0CRfbkF/mt8GgAZD+FwOE+ZNdtYIsSFWhcU9bFGvXMYzhTkPdHs6eRAQW/gBDDqaKxUWIPgIJkURJU5dyCZRkzyljYElVdo25rIp8yI/yWJeNLuu9MIA00u5fOOjL8LPGpQlAb+0t2eJumHjEG+vehx3AccPp8yqYrWaWR48cDe9wvcK7K4WCS2NiMc54vyzuQypV7IwRfclu9DfEZhhPss81IjC0MvPPZK2VhUus8rtLueZgxDVNWExVlkd/d3QORkWNIGS4XbwRtZiJwVyWMtswjwdXIVjxgRMWwdTsMXtI6A770z6/rG5LJAAynPnODlCEUSQjC3nkM5xn9KxGTY4hkprNrgEegqwi18yGgn2ecxhEfTycqitgXILB6xxh6PrXVV9kaMmITci24yCBiPSkcQjgQ10VJIVyiKKrs6tjsfrvo+epbIa5omp3qthiLgUbQGuYXfOYLnsHuH/fY31MnXBiDfib5QX+8kGlLT97G09xjHC9ZC9r3r+hPb0j3OO9QNhWMWnX9Wy17kAqNNaxQ5CMQQkRZFbkyu2Xlak+v+mNJ4RMSiigPfsY+TZLIJkEtgQkbNmu3rS2gFW1mgSNHhdVrjEaMO6oEmwpTP9GhyvAuabg9E7zYP55lMcYYlpYUV+S3b1kxUvazLQtitPsAtyBL+jLhri5W5jwf5gCNGnb3HXYPOzQ7GvfMTMxy3iMIatCUqJs92maPZRlhbcEM4Y2JCsPJ25dfqdXvX/zSxbHPc6iUUupnWQ6/d4kRCQCEKEzyhBiIsZ71xJpULaJkIQfK1c3NGg2ryZTDao35sMP44wPbzlIRN56HXDR7HiWVrxe6j/banEi6vamfsn21dGbLOJOzJcOdt64toVPQNCGb5SyJze8V6abYrWZNsS2zppsCa0yGz1OSAphcImNboT008N4TqmUU9Eipg9IR2cIwYTde1TTWruMGkVRJgXHL8n7GPBho61H4gi3KI7Reu+irJEz2C5mGcfVrZ3tm+r18IDNHAEohuJC9OmQcZW3FvBJCM5Zlger16lo60dxbVAsFH4gERXukSGNFKQpvWdN0gTnbPLumgz/krluKzWVccrG5TAt8lpOtHJyO9/4M9YciK7fE5XC6jKi7CkVZQSmNxEWrvHvaqI1kleTfy7SQ5bvRcNZBjYBzgDFEaC6KKssov3VdXvssz82Ib0B+54bzkJn02mg0kXhdwOq052PAEgIu04SXy8YXwAuSwY2ZJudVKuwWaiJy1owgtl823QpVU2OfHlGWNUJw0Nqi6+6I2MdKot9av+Pg1+uholcfZHnrTKG++P0mQ/xidlLvGhRVARcChnEi56enE/pjT+xfN2FZZkxTDzECGccLpp4dA4c5d9JaK44dXOVGV0YOfCg7uPxyENR9G+Spjc5hQ+KZbgqbiwxxlPqys5DO2PMcLjEZKSUysFCVIh9zW2aIWpLQRBLilcoyRDlElpH8AYjf4Pk72aASmkJixCZUqulbFmmEdZ6TbvkDQiLKGQ1y0BVr1G7ZlJl415QlfKQqOCZg4Pl1SkQMq6oGTXvAvEwoipK67RjyXHC1glVQZp1pigHUNs1w67QokOAtqz1QF+q0xbyMSIliQGMKDPmukaM5nc2uh02ez4F+j2VvgV1dY3jc5+48RSItxZh4A+S8cTaA8ZtRjdIqh6iQgmPBzPLCmUcAAgGHEL5q5PFrS+JIU1rzEbbEXtkQheVOKFvYGCrJQUbojWRzKG4ahDdERXnKMKUtKZSFlDGRC4r18ExJgp00gLUIz2lnVZEjUA0jZrdev3MOehN4Ira00vys9yDmQ5D2M+rYMxvcFpxdYWg+zxu9dMqezbZENVXF9ipnQQ7y9bOl1cWPxys09yaof2ETr5ud6+YRxhQYLzuMlzGP2WTfkzFvZs/LZ+dmpaio028PHe3/XY2isPBaQ0fiDDRlidIY9Fpj4DOi7iqU5wrzMnKTxLD/F6FBa+HJah8h8s4WwRVIiZQD9Y0GRuN5gCsLVKzOksLbMeoyD3POcNBGZzJ3WVKIUEoJ4+LgY8TrMGA4Ee9jnhZ27KN3whiSrUOvfvvBEXcj+pjNoPK9ZkM674h31nQtypJ4AKYgmezduztSFTQNsPz6qOfrraA84EZDb6xitx03gNx52QzxkLc4OZwR5L14j+kyon/lGzHO2f+YLD9Ji07pTvTPeJkwXUb6e6oCWvNBKJB/TIhmTX76JUifYJXbNgCpco1lmRjDTvKztDX8Eq6btfjYCy9ijeQkolJRVrCpZI9ne/WZpXstjCXIszCIwSCUlswgJG0uJcSgkXTM1px0EJIjlFiMkmf3jR0/SzGFxAJg9WtI2DhG0XNA0GqxQt07Qny6+x0qa7H4gJhI3jQuCzP9aeZXFnW2wDTGoiwbGEOHoYREhZw/j6vDR7pQ+lwpzwAzJHvjjF/YttOgkRCzPI4O1QExeKREv4eei8SbusMyW06PdIiJfLjrgkZdviDf9umuy/IngPgLQugq+J0RZrbIlLK3OUPAAvMPZzJDmkcxtWEY+FZJk1q78e1mK6qJbXKfdKsCLwsnCAA0e7N/maUgkbTCl6ENLiK7eRYEWYaCHM+ijxy3inzgyQxeeCxiDZ4z3M3q7HnL9YuHQQrUcVNozGqLa6xGUky0mx2WWchlPmcNVCXxG5rmgLJs2OGUIfkvQoS0oSAc1ShEvyEt8gzcyKgzhxit+vUgaidP0uVldrkD/9bl/ALrZrhlzj4rtjCwIf6skMrKGb266ZV1iXrXkF8DH/pGa0TDNuXGoLIWpbWIiTw+RJ7bdncAwHwa4SvMUKzqIULo+h3RPVmjbqWjLmviodyy+uMAW5JMXV94LCVkTk8Kr7IiXwnxNijrEtYY+BhxniYYreG8x/PlQmdYP8FNLo+lAKAsOYBLCoemZFY/7RuZx+PEOG9hvkfIPv9lU3KTVaG77/Dwh0fsH/eoi+KfPPi/IIqtcz2FpK8TywQeER2z+Itrs/oxj5fVtjZtNo91juowzwOmqaf/7clFqb6MJOVgg56iXF+MrVWuKA229oW+uD5cv2WJPawECGm2h6Rbw8Ei2uM6Q5x1qIwy5DQ58IZhivwA5INJrDhZqmE0wcOeN7gipIxyCEScCwvuzOnAKHP0bcEw/61wJyEHEs6zieS1a+KfXBc5TtGvCdRHutZdRi18WDWxPqwHmS0MyqqiVLqyyVCdNQUTy4S/sfrHY7MBbXXLXxqa/DOr7iqGnNcgpDB56ui8w6JHHgF0qCLlirvZ5MMreupog5AYtYbRCj5YdFWFnje7ZiCYXvGfE8MWpdSa1sabQJ43+5BdGofziP6VNhiBl0NwSJENdW5YxtAYD5v7CmC12t64oq3y3U3mOP+TEKHSGi8sCJVnhdBKUvR5Y6OfT26JVEAneEUbHmK64tVsI3+/XL+UcX/LkuefkuiYlxMiYiQ0UGR+MdGhY22BsqwQo8/KlrbdryRUs7HgNdcR19oASlsoaS42vydLVTeoUowRcFgLqSwr9DeHU5EccMbiJpYnLph6BbP4lTfEpmWy14GLQ2tNNpGpWpo5h8ABM2zQVlrLkDhB4wUf0qKKIZKe572diKsyahCJplh3K8X8M61hC1wlQd464jw/n6/GuttkSTkHoFbL4Bho9NArBRc8Kku5DD5EjMMEN1HwkqiRhHskjaTY2FPaos5eLInHO8u0EnnlnkvGi5Bl665Gd9dSo1V9veD5pjuTq/8NlJkCJeSJbe9WxyxRiUrTPGseZrhpoS+cIeGtBlUpxYx3gsXX7mrV79Mhx10eV8E5MRAeKq2SNqV1Tqq6dQmvIaMcX3aTIWaJmS23nbfMnA0TmixsUTF50WStaYwrHCubQf5yDP0dKUSkUnyzAyiylzoteRgAcMwjhx3FmFGRW/e+L6M3lVI/Qw9EZiLzRqlE7YbtLZuy0RqFpUKqijE7NNJ3KZK+1Z+9rFjOtDHH2ZoW5Q4yxpz4J/Pf/28c/FVDY50c/qFFLrWwZSz5CizLhKaeEcI+18llU2YI3Giy2rS8WVrW9tOmEbJdaTZJ+gJGjpEKTOm+xOVNwrKIJEuyUueX/EwlXEeffstSvMFuTai8MPb5vbLMZRF0S7HZk2JoUljWRoy/mjITmdbY5dWWWnwyhORkS4sy0uenkRsXUCIfLG0mfMpelMdeSeylb0c8Mvk2iomQzTkIKa124VLMGlNQ4ao4bIuTF6uqpXRC9vgvWZ6cUkK5FEwU3Vhci1Mgj46+jO3ORW7iSGsZn0R2D2XS280rkW/DPI+Y+hlFNa08C7OGq0lRUmxlZ2aNKaaxY8xcA3E81IoSWH2gPBXhI2Xny6nCPHFGRAjwYBnh4tcDOSMMtL9RIURFd1EROfpW/5L+eKFRaU0jGnl2iw0vgc4Xao7Gy0gcj5EkmEtbZcveL5uQ6NfkvJjTWkNuHA0MfOVRzBbzFyNDGWttD/3u0KI5tPnwL2tKBxS7319bXz34g6c525ce6NsXQJym5Msjz/KCPa7tGkBgdTbvoE5Ub14ufonSmgIm+dy0GSLbVkq6H/2dBm4Sy87En1Mj8aFJ/gPXWfLfsow1HBd7PWdSWgERCN6vaXmbAqju6NCYh5kPDuTPSIcXXWeKkWDkKHG8BH1qVaMuS1ijcQFy0SMHw5cdt8CxdEABgMTY3m5bGmOECoq7mzVuVZioprCw45opnw+rsHZBC78M1hjctaTjDzHipDVOdZUNXehltnkjzfeTTXFEDirknm1BQjr2axljLgzi7eZNdVfnDW+VsFIefYiBXPdiAJbpelxjNGruXLXVKBjBSYkkPpdpwmmkbt1x/oVU9MbqbJ5TNiUzmBm257GHoGCi5JinCfMy5qQ6/jKglYE1txW9UoBJDgJAm0XQa9R2YpjVFAY68iY3uzyTdm4m/4NKQrjo8F6mJRdwUrTT5qcyyhHzIU+brPU2m0Jd+dVvCkFBvyRR8J+J5N4erjEGKK/gowO28i7FyX2KkuIKV8IvJcaR0MqrGbjiMSF3eMJ3ENQDYKnqsvABa2EKT+9HXUJZgdORnwX+hCviydcemZO0JWB+y4opAFHBOfLitxeb3yFJCRRORcmIrozYAKzI6xfvsjE6Q/xK0eHko2RdFKgaDrqx1AwgIKfdyf2SIJ7c/PCo0BgN8AhEitJbcxqG04iiJj29LyyKUOT9pDQl77WiqiJ0ZB5mFEwkB48vbEl8A8fvdh7HsJ2w57HM1E9Y9ks+P7tDS+8eRxV7JqenIAiLyeeodPxlI6iBIWLkVwrerx78bl54DsebO8/NMnFOoKoNZBWZUS1GDoISNNzlT/3MwTKRZStTDivxfoFWGssysqGD44M7ZXg7pZS/5NKulVVut5xHvHpBb7fu1Fpj8RFap1XeJoEQMSECKCqbA4iqukTFX4hSCmd1zl+imEu4ZUaInmxQITaocSVjxQSrNbqqolkNqItdNrpczXCXFF/bjQpAJuWRvv1GgpOQSsLq4ZAsw/P88hrWYmcLZen+AuA9dXfGGNw1DX44HFAXBRzL4o7jyLPADu1dh7KsobWmA0OiWY3K9pnkXb+GJYn3gfc+y122m7JiL/9bZU31ruFsdJ+7zLIuUS41Fv6MIVBanXMLdXxsWGMLy/GhBUsYKYZ48R6Tc+jHKbuvMXJIxLwQUXd1nvdr7rBEQgeIg2HYbMbk8BZDQIieSKR8SBbFbR1/fgaYvJfvqQ5UnERCA3ImPUsoifyV4JisGwIZH8VAxkT9cSD/dbNC1TldcXNQxg26oMr1OVtHHZET6Tb+9HxftNFQLLe89b2nZ2kdaUWG+VVUxCbXq4RXIGVxkJunCYHNn/LYJafnyT868xSKkkJ4lNG5WJLvzi8Ngo9oAJRNlbu+XCAzygGsxmYynorxtoPfLTOMjVgWHh0tXUZ33OKAmbxG6DCKEJKnWGRvm6R8jQWNt2SuH0OAZ9mb+G3I9yqNlmGlhkijZYlnxNVoaTM+ESj+VrTHzQuRdTlhVj6fX/yVqoyI1p6VWGtqpGYEozCWbcxnjBdSA8zzwIY7hPq6xWM8DTgaep8Obw/cvVdYptXfQpZShCaK4oKQiDUUSFBz8xX/jt/V8UtlLtID+pJ0TsqKMUElIr+AIRDjuQrkQ78qixxosUxzTr+al4nCDjjZKcawumX5hdyJ5mU1EWLd/hYONTx3hMBzX8x/gdttawmCC8Bmfp/VA0xsqbuaLCjvOrS7Bvu6Rl0WmBbS11u2dlyWORc0CeRmBhAkuHDIx5bsoxge7qpqfbmNzAJndrMrs4FFdtnLxjg2yxxvWTEmaMSfbbiwQpg0+UUQHapbVikXfV6NfdvgcbfDXdNcbcZGk0yH5lMdDocHnE53uFxeyO+fWa1IxGKu2RkrVBGXcso/F0BGJbbIB/2smA+ub12EGIWM8Ai/QSmKADXGZumRdJ/WVhTucdehu+vQdDUKJv0ktyAm4jfQbJ6iroWM5fjgkENFWwq3IpSlQFGxx8NUElEoRkRrUPGzH0PMM17xHLjdsneDoMhzpWOed8t3K3C0PLckL53zBid/R/ABw2mgwKa5WmemakWuJPRI5tUIEdt+nQ42xRLI9b/LHpSLz0S5GttC8FvXum+sbqDb+6GMYq6RRdlUeRQJiPSTnpuiKGFtCWurXLy4xUPzdyWyRMlA0ReNmZMQhdlfVNQ5SiQvgIyGbveLEK4Pui8jzX/vmpcRJRJirH+xcFL5PfgCdTQrAZGexZDNd5qyzGZUi/cYlhXtmgciEQrSs/2RZPZD+Rwy1pFDTrgFXy6R9N7KcQhcTIlSR0bbMRLjHgC71RJTX/JlgCbvFUZpaKVyg0J8nImb3AVFURKhnTNZJLAuhIDd3Y5dJwk9XubVlXUblwyA5JtcnNvIMmpjYL/iWvi7n4yV5Zqg4ppGFFPKf4tyyLMdibIsqwJ1VXKnFzDIwckdUdcdsCzvoJRGWdbZq32/e0Bdd2RKUKyyDSF4bGdw2Pinf9ndSkei/omZb2byMrxluQODIjMF6lhb3O93eLvfY1fTC/PxdOLOjC0lhbS4jFBKwzmao43jGefnE9o7Cq6QDRUAmpJmNnVRQHWk6dbGYCyHLJ1aN/uwISFx1283pLhvXFpTEaUBkJBghRNhcPV3C6pimWAkc6yqKXHftqiLAj7STE/saPt5zsYlBbsV3l9+WIk9uRsgNMdojaqwsHp9sAUqjjZSN6ZXDb0UgNHfdvCbwkC7tXBS/CyVZQnn6s3YhhzyiqLO7nSkxoiY5wWvwwBrNApj4YLHy+sZLx9e8PrhFefnE/ojWb6STChy50yfvT10zJHh0JO6ROQkr3kwFN7EHaiMIiS0inwebrv27eGujEbijhwprXN0hpRp7MUsbE9Sx5gCyZUMSTW1Zj7DvDADW0PxHpEJn8v1SE0Of/l3pWTUuKI6VwRhlpde1To3HvwAGHVac+Zzh2lWzkLZUHyyjLZSWkPCyrKB0YaIfcwXoSbKI0a9khoXnztngKWUMcB7agrCRiWRpatBZaWHHHDynUmReuuin70SyQTdlSYi5zJsmoqUEpO7i9yNW1bhpJjgeD8IMWKcSfdP3WzM/y4HqJDllCLzsubQZJtcQbK2fChpdtKm+Fqm2y2Ll2VE6Zlbotc9JfqAOVAuxsJ24W5xxPC3BmUzoxiKPK5LMeLlwwtOn8nA53x+xjieiPdiCkzTAKPJbKgoKpxfWgzngYO8ujwSMsYQwsX7mBQTK9cCSGlNiQV+mey6Xb/r4E8s3QLWDitp0dTSxqe0Bjaa2mxfumtxaJp88C/e4/6HewQXUFQFukOL/cc3OB4/oe9fMc8DlFJomgPu73/A/uGAdk/zXUknWvOoFVfCK+9ALlrIF7Ju9W1WirpSqJWFKxnokjPf3Xe423V4y+EMTVHgNI7wbPVJ8x2feQyKP5hzM4bhhNPpCdaW+bB385Ln13e7LrNg66KE1USO0UZnTf8yLdgmxq1kq5X8dsuSTTkp6fx/dnOya10M4qhH+uQcnsQF43EYcBrJ1tmFgOf+gtdzT7GSx54kO0aT7XFLkp6iZGhTI7/shbFoCoLPF+8xVzOWcuUGXBWEALOub7v+si4RXMhSKltaFI46PHEDFNhVa43CrmRGxyFU9pPBeBrzMzOPM46fjnh+/4LXT684f6brJw+LBGEym8904C7Tkp3a5J5vI1Pl4LdMmpQEs2WcKexpuc21UHHBR7I484sKnPX3aii1ImvWWg7lAeq6xf7xgGZXZ95PWReo2jqTNQVdKOuS7x2NBrbwPzbd23ack7QCQlqfwUhopOxJX4sn/bUlOnKVD5lV1lxwPjyx0Om63LRgFjdCY9irQ5M/RXPgrl06NgCIuViQw1+uV65NKZ2bLUAaD9r/oo9QWrhNa2GwXbeOOULwWXmklF5lknaNTBdZ4vbnWCZzayb6Si6D1dT9Atwogrgvla4ArXIQklIqu5ZOPcl+i6pAu1/VQVLg8R/I+504mKbks6WwRD5/65qmHmXZwLsaZU2fV9CI4FYTpuE8wrsFVV2vaIfClSPj09+e8OH/fI8PH/4dLy8fME2XvF9IBkVRVGjbA9p2T+Mhluwd3h4yugKs6HtKiSSrw0zkTy6AtsTrf5rcRxIlrKE8G/mYBZBMQggMi250/jLj3NU19k2DpiiweI+YEtwbgrhkdlvvG3RPHabLiGVZWAZToN0RXJqDPZoqz9REpvRrJIbtKGBbFNyytCESE819dIanJUVr1xK8f9+2ONQ0248pwTN5DwBr02s0DcXpih+5jACG4Yzy2GR4Ttz6mprm/BXP1L2QorIkZCVOBec5Tc8jhl+XOf3eZQqDtHD3pdWKmmj1i3+vzNOpQ8n4KE7TiNl7muelRJnSlwGvn444fjpSRczOViklQnoswXuWzYOij5idgwseTVFwB70SpsgwaXMgJHY29Lc7mBVlAV95lHWFsiHHxCQjlUiborU2v8hVXWfGL7myjYg+5u7QGAM3Lzi/XHL4kvBlpICmLpkCiYYjEcTIC0MsnOl7qTtCHAIHpmyDTET7v9yo45alNM20FSNqV7+Wxx/r5i9kPLFXNsZQTCl3MFvFh+W5ZErke4A8OjLQk87R1qvrpaCNCUmv37HA3ZGlojHE3KGLxvyWJcQ0rVM+AEVGV1SbGWtNBlyRn0NbErO/bujel2WDpmszD2CdzdNoQ4yXyP52Ro5iNSaPP+X+Aivcn+f8Qrz1APRG0cA+AbcskZwhUVjWVi8uDqXS1QNYzWyy1wcVKVVbYVdXKIzNpD4fQg7oMprIfjElfD50ON51uLxc0B5aDKchG5QJv6duyYlP0MSUVq/+ZVrYNtpnLwN34/M/DGdUVYvgu4zgpEBolpscufdd+sxhiSmgvJQ5Q4HCsxLOzyd8+usnvH//73h+/gnn8wvmqYfj4C9jDIqiRlnWWTmm2eVy3tWYxwWlhAEp5PdBsjNsQV4h0jCWdZWfBxd+u+D/6sFvywJm8VCzWmdKm8rUyOw3s2vpzwnzUcwarNEIkbTpAteLPrLZNYQAlEWGKZVW2XzGFpbdmXimzx2zVI/bDkRgXrk52pr8GW9ZysjBqrI8rqjKTORrWgoeaqsSDRO5lhCyK11RkZnF/nGPN69/hlIK09TDewdrCzb32KFpdigK0o1vLRtLS6SYrqqoG/IeZgPjCcyrlIKbNSCHnAp587sV9iuYwCOmGBCZUVZ1CKdi/TPrAWDypngeJrws5+wqJ1nll9cLOziyBp190Ltuj5LlKcLynkfyAr+UZYb6TSZIGZhgQbsf8yNZQ79M7uYDUBvF+ddVdtNKoldn8qRfqPvO2uGaSEhuobmcmxfOdSDmsvxesTE9vDlgHmdcXi8URvVFQRXcyurPMLO4wIEQOGG5J+bfiI/7rf4NALvUyYjLaOjwhexWbXz603XBL4l9pjDEc2A/h7qts7lOLs5YzpRntqDNMxZUEMjzlz8XH0Zy8KUkLoCrxTB9aEboboxkjilAxVXKS12vuYpeLjgbQimVbcOlQxX0QkKkqppIWDKSoXc8rJ+bXQGrqkFZ1rnjN0YT0rmRxRIao9lr4TqNMsaV73Ir2pOSyEEJVpexrJDJzBeGWZ49Wb6UDst30RQF9k2DylokkIwPAKzRqGyBECPaqszjO9lbBKq3jPAWpYWtijzSkA7czQtSAmbOsHfsiHhrLPE8D0xqXFUywnNzCxdr80BR6YrUMymtuSki8T5+OuL19RMulxdWeawkWUDkn2RcJpLPoij5eaKRgjhcrlkBCxJi9hfYyqVlz1lCgPb/JLlPJBt+8Uhx4a4eRLzZQG6ZbY9rHW3g6sNzstjrMODyQrnNl5cLEZxOw4bg4TOBQ6KAPZPGlsmhrMnBTUExOzRm9UCKa+EBdnKSjvHWJdyCDHcZDoWpKTa4KUtU1pJpgzbwMWBcZkyOHrqyKXF43OOHf/sBxmjcf/oB43iB9zO/2PzltzTHag4NDm8OODzu0RwISbhrG+yqGkZTpHHB0D8AnHENt20/t0BCtyaUmcJAEYfuGkGRYsjonx1UxmqYgmDc/f2OJXGBIkvPQ3aZ6489pgvphJdphlscz/QompVCVtgNkbO6V/MTZJMKq+l7kcMxhgjws7hNEbtlCTGpbCpUE0NwkQ5WsZYVVq/mbtVsOn76h3kQ/F3UZYXd/Q6SSAal4BdPMa6fT3CShT4tQEzsDMlSLobRhdUs0sZ8wKWUpT+2MCvp9ZZrT4ACzziZKxJZTqTNCn3HmJCC52AgIaoVKCqVo7KlM5XniP5+2Ug93LTGOys+aJQPiBujrO3cX8WUi83VyGpNYVRKxn+/jEz97nsQI0nbAHZpK9ZkQj7ISTa2IiBFXUCb3caPnpMNS4uiLtl2XCMAMNZSxkkSQ6KC7/HKK1Lb4paLmO0sX0ZgwmcRVC762zv+lNLqlZ9Ww5hm12wO/lXOJl4qwKo1j5EOv74q0FUVtFLZx95qlsZZQwou7zMZLjsahjVZMwZKpZOCS1fbwpF+rhT3wfkcKezdbe+99wupzIR/xF03+LwRHw+tNY202gb1JqCNvDkcFyTkpVHX1NilTmLrS9R1x4d+QyhR3WWfghgjmd0xeVCs0WMKWUFUsKxa1GbtvuXm5OuN7ldPhJIztjORxIf8g1Ik1u2XL5eYc4QQMCwLmzUEnIYRx6cjnn/6jOf3LxTScxk50YqqLDGDKcsGTWqxzGVO8ivqIkOp2wdMCFFbxrF0/cbe7toHrLIYmXEJ07OopcsvURUFSj5cfYiYnc9VrSkMmkOLH/7tBxzeHLLbmsz+UxL9f4G6rdDeUajNw48PeDzscde22NdUABQMlRW8IQpsFkJEKuPVBhn0muYkznnfuraHfb6nZnP4623GABHSqoZY7fuHHe7u9qisxWWayNVqchjOIy4vZwznkdMGeezDmyBFONek4wVtbm5aMJyGFcKVmZY2+dAj4hR9bjHzEWlQuHEDkAAdMSmxJbFuxTY0NiXxN/waFa2NueJZGNDGXTVEAu3uOzzud7hrWzRlCaM1Jrfg0+mMj08vOH+mAqA/9Tl6WMY5cgCIsYi2OgdQCdfC8CGS59H/RE5DinT/jTE82ojZQVGgf+q6fLYSFVmXKSSmN1KYiSYy21aKRd2Z48LP5xmv3vz922dPbWS5AvOvhMPVvyDPW2+c7wPIJjwZSdREVivqgv8pqUBhjkJgyZe19krSK+MMW5ic1qkUzYytpcLBNRXPp9MVYe3qu9gUPr+0sQuSIL9/Wwh987VrC5VR1etUuKqtrvIaCFWbc/S5mHgBIAKaNXgxNJqtigKGCxSj+M+zzLWfZxwvPcYzWboP5yGPDInoSyl4ZV2iZlKbLCmIxFZ5GZcrK+xvXUopOLfALfOKtpn1Z5BDo0ZZVuj2B3SHDvs3B+zud7CFwXiZYOxIo+BmB6UU9vs3ZFTEB3x2t61L1vtL+BaFPS1szgUAazqnPAMktSxGep4S+35IoUNcKEOpRb+yvnrwZ2i7XRmFNHPbkG1kzreRloju8aJGXEBBO/2xx8uHFzz/9IzT04k6wHHCskwMr0yQEBuqlAqSQlQjG1nwhsfhOMroDSyeNhU/dyNA9nK+1cyBoBSwH7x4ZdPIorIFCmNQGoOCpSrBe/gY8hhC8eyyPbTYPZB8T77grAONMZPHxKim268HQ2EMqsKiLspcRPXznD9HPow1WWYmljvRqKHI5JlvXeL5bywhKVvvBiFXxrDa+QoMun/c44f7OxyaNR3rJOYS8ctxkM7hKg37e8vnTQkZYp/HOc+UDf/8tqbfJ6RLbYX/4JnhG66kiN+6UqKMhqIs4EqHsi5IRaC4u0n6aqO+mnkqBQOq3uu2RnvX4fD2gLf7Pf50f493B7LWVFCYnMNjt0NXVXi/a3Iw1sJmOClhc89X5zxtiPMhSISgbNJdG2tuTiij7p1Z3Kyako30qui7CubhTZI3fnGRIy8Qj/Ey/iJKtDWHUkrlcYnMkovSZoJm1q6zt4TA/ACu7LxlRHjre69ZWkyH6OouaMwaxGQyysLXn0eUhAZKPHD+c2xOk+IasCSx2VLUUQQsfYbAhatnhYZ0c0EicsO6x2z5Dil3zbddu4wbsqFWEJRrtcIlhEPDafa5sDTbFz27JM6NZ0qkO596lkauoxNgNfsRhEDifcfLmJ9jQa3G00jGOEwgVFrlZz6wx/3CyJzEk9+yhNhIzrHsWMhqKjlbrC3Rtjvs7siDhOS7rLbhkaUtLbr9AU23Q1WX6O53WeYroz65l/Mwoz8N6F8veI1HzrHxVz4N231sWcYrFn+1OEZnwK6gv32NXz/4tQYKXKXEiWGKmGVk04TtSmRwsIwEuYxnyqF+fk/yhvE0YJ5nNrlYcnLd+scJUlkmS9DnOGPq5xwCA54nChwkn42kPDybTKvM6dZoVoHmAGzgbWYvG32lmYwpsg0lw49JiJAKhbJZfiFwcHa1UmvYBkBEydJaaPVzqFJ+DzkcRh538IxVr93O9vPf2vGLY5vSGgrrQZ3DTxTp5HMuQmnR3rV4d3fAY9dlJUdpJU6VPqekN4rWWls+IHcU6iS/V2DPJS10+A8zd/iSaaAzfLi9T9wE5p93K8Uj+MDzanXV2eYDjme4W6KTd2S/CobohZjUHVrcNQ0e2ha7ukZTVqiLNfZzV9c4NA3GZcH8sAeUyqMQiqldVSrrrFcDkEz4mANyArPkxTnzlhXZt4Pm9gbRGiiZ5QpbnjuxfJ9ZaiX3KiXkgyOwROuqSFerAkg8J7ZFQDIps+GVWgmjIYmpVGSUQcYdCpYLXbGLvvng1xpxo8SRMCo5tKSAEZfKZaLvSRoTtTnkttC4yG2DIHXc5Yv7Wo70DhHztKzKhs199luVCr/3YLmtFEKiCrplte2Bm4jVPGx1AzRXxb+MaMTNb+sWGEJAGAKRtnnklvkcfE8yaZF5A56TRyWJTikFxfuBmxfM/USKAvYRkBAfOWvcRIZe4qNwy9rmUNBn03lsbCx5dRSFQnNoUe9pRCvNimOnPWMoO4XcCCk57/DmQP+8PaC726GpShTGwIWAfpzw+vEVWlPBL/kEzpG0EomMgbIdtFsw4pLvZ8uBYkortuz97e/+q7uCdJLyAgKAXhRchoFFW7seigDYqMJl8sV4mXB57QnePw2YpwnO06wkpZiz6YXZKMYjEsvq+e9ZxiWbG2wPS6lAN+URfTaloRNtIresqqngtMuzXVlbkpFSxDcIkTkN3mdXqrQZQxgwglLQoU7dFAW3pARirftV7yqFA/EkIhQo6pEY8hEhRSze84N+PeIAS4vKpkR9I9ybCzuWFcmzINnzSikE0PcTQkBpyHpXLGoB8H2JGTGQ4A6R5oiDmeSnC1QeQ2LTphXajUyeEcau9wGm1Pk5REr5oNnCnjezmzfjmoLdw6y1cNqRFjuQsZAt7VVxuPWUb3aUM1DUK3nJx4hpWc1tZueweI+K3c12+zZDtSkBxpmr+w8g36PgfB43bDtPAHl8ctO1S4crRRbo2ZIIWHnP86xf/AcMWLe9MXKSX/eBOrGNRwBAVtwo7EoYiwlJpZy4Jp4IKoV8D7y/5g0YHvcU1cbtzdqbzZsAwAcHA4uU5PC/1kjHQMqRZSQDphQiqZyYWOqNJ5mtDlf7oqStie+G6O5jiFkH79JK9BR/hODomVsTAmXGfz0GEBOcWw++rj0gcjz6ypVZyG3PrwmF4jUPrHHs1wFmPgezTf2Udfv5WZbxldj/stOlHKKGC8VtNLjnIksbunaKQ2ZVxETy5pSfi9tHPXINYrBUlBahqVDW61iqqNaRmxD6ZIwb48qNKHn8KRkCVVejZbVWYQxsCJi9I7SKx51jN2a+G123kLYV89siI+QJZVmTp4a8q5qSAX9r/b6D31ybJUgXte1WReom1aAwVSmPPuSunZiHaWNhSeEKSm1NMhSRFwrabAUiks1NiCsyL6QPGmCSyV9W2nx+wyYSt6wtcQVgXXiIcMzc186hNAaeD3H5mVZr8qVvBaKk7qWpK1RMzpOwFqM0QoqwWmNkbW5pTU5zkwLHRzrohSzpQ4SPIaMv+f4ZDaMpo7msCspmnr9d07qFZdfvZv31vAFskIsYyKxjdC6PJQDqCAR2FkKcELmkS0gsz6Eiz2WpjhQNhg+HLxEmGXUA2HSU6z+3zviXcUZghnbB3bO2VPgsk8vPoHSrhpm2EktcdxWafYuG3RyFmyGHvpmJOekDfa+LDyhYxTE3NOPLBLqNVFYblWeApAF3ecYsBY/SGtaom6NJM1mL1TX5wF3c1fw94Zefjbw2xWJKCSpEJKTM3AbEJ2Ql6ga/BldtZ+zJr3I4+flKK3qHCktyM4ajLXeF/isb4K8ta0toTb4TqzXuOjsXnwpyzZRMkfXgFdvyqZ/yZ5W/S0y38gHF75EQnMu6pEOWMxxEky4jHUnqoxCwrelPzHsBJRjedvDXzR7OTXnM4WZHh+swU2HODP4UIhU8aUUDbGHEzQsAkEZi11PA1JyVPau7qMnvitwLcUMlZ9LAIzfibATONpBn5ksHTCqo/rmQrlVOue5LynDccFfn4lXQ7/E8Yu4neEff99RPuWlKqaL9eDRwNTWu42kEYsLAmTMxJQwnugbPJGdJN7WF5YZXb0ZtFlppRJZ0S4EvygviDf22kumrB39K5EqmrIJNm9AbHVaSFXdq4jstDNSUqMPVYc0w7u46mpnOdZ5vX8WsbmwohcDnpdMrFhQVSf6qsJnvyp/dwN4prB3LtiP71rXVBNPBFrK97lDSzF3zIW75Ya4KS184v+zi1V4VBUp+oLRS2dTCc3cPIMP7RvEBt2HtU+cfMC4Ow7JgWDh3e3G54tNGwzDpzZYWbVlhV9c3HfzWSvW+Hu4yRpG1te4MPmAaJrwYut62JKQhpoSqKnF4c0C9a/I8WF5yYafTA0732C8b7TKT5sqm5KS+mtj/JZEqw3JtJXtFhuJu6ZY1XiZ09z6PI3LaJBdikpvtJoeyKbPR1Jo/QPpto0iN4ULAeZryvhjTqnqR/AGAmcnjkuV9tjDQGymYX4gAJJvNVVebVlmdGA/dssQtbptxnyOaN+OTTCTUaxccg8/XqFRCUorex02nJzwFMT0RNne2mZV3x2igJAlX9AEByDA/gJ/H1mavACrGblV0NF2LZaFsDeq4iSQqCGQIEdqm1UXOmixzpu9vZqVDys/69vuTgz+P7pgUKTwZ6XDp0J3ywS9EwaqpAAZzyDwrZmkkEaTVzcTO/e4B43TGskw0sl1GjJeRSGuFRUoFNHOrxEBKKZH2hYz8ksUtPcvjZcRw7CmQZlmQslqiQFGV6A4d3OJRT/XGs0JdResqRYY9RIymPWQeZh6JTVdmaeCi5ZZVFDWMNvnnySEvfhzV4nORMccJ42mkMQTb0ROKnVCWDctx6YyznPS5zI59EdbCTYoGaig8jYc3aF0MCVgc804ilDbQibgGZbNJMGUCaeBR2q+tr3v1B3Iu01oDlh2DCoMQDLTANkyqEYJVURYo64pmONwhS7UkMK2b1oCD/KXywe0XlyvJ6OMKkzFhMId6/IKb15fMfrH5tTdugFKJikezfD43L5idywd4aTlqFYrqGL3On12gB/Q0n7BMLut3gU0Hw8WPUiq7Xu0fdsR2HUd0VQWrNUJKxJKfZ4wLVZAZLmSinBCQqqLIHgC3KNlTokM3hS/kVFsUQGsu8lJ+KQEigs21h+aHUDP0LQeJzC7zoaECgjfZuIjuTYJPXNSU7AjXUhddtRWqwmZZpyRfbWfOSAK73rb5zyNLelzg1DCd5+aGO555mJESx/DyaMIUBDFnn+7LmE17xK1N2MdERlqh+i3cbazB/nGP/eM+W3jKrLM/Uoew9bxY7YqRDXRuda6T7Af5no0xQIlNHoPYN286fq1yWNL2YM/hXTGhqOjzWU7ztBu5oi0knrXK3ITIz9RkyOdegozkmVdQG7mtWSOhOYr71s6vu+8wDWOulyMrNbxfGfxSYJHDo8eSmGQ2O8TQ558vHa7M9wXuFzQrj034Oyvqgk16kAsH+XPye8VRLu+boiTZEDCb3W3Ezru3DyhOFS7nF4555u+gn0iuFslkSLIGREv+JZF2vIx4ef+Cz//4jMvrGeNwxryMEC6XUhpFUaJ0TU7RdLMjgnNboWyqlfPASO4SIgBHIxTnMfXzpjCiZ0Oq0ltHHVXVrLwOaT54n/NMdBdEZpkoX2IcewzDGfM8IAQHpciqupn22C0HAMjs/ekyXsl/heNCnX7B359BuXjMJSnaMqHeba2ULd2/epPUVxTZFh3lrxd+Xz34ow9AXWZiGwB2L4vZXEAqPGE/EkObnPYkf3lyQlhY51tfbsieXd+E3DCPM/khsxFDSin/OXlprshbmw0IcfUZ38qDvnXVu4b+jp5sWOklS0y8IDOdmBLNtRX9u1gTT87hdRhw/HRk34Iz2zz6PL/dOiEKEa/ZNWhnYrMvuwUvdQ/7BbztI9myykZruOux1qIqyemvrUrsqhptWeJ4w7W7ecm2vdt5qk4qz20BJv8pkbAteWMUUpp4aK/jgGtCWHKJD+2QZ+MLd7tSINFGLy+gIRMf9k1wi4NntQnF2NLLH0LMh+wtqz/2WHg8pXneXLIWmwiIoBHWMEOfDTl6nUcMpwHn5zOMNVimBf1rj+f3z3j59IS+P2IYThjHC6app2hfDmMhN0cLbci9q233eHz8Ex4ff8ThzQFVW+XnOLgAN9EssWxKKAUem1CBUrK5THEjuQ8gVYe8qzbZTKyE3E+BtTfeBjKaK6qS8uebasMGL7IpFyXSFTlvPnOJLJFllVKYncPYT7i8nAEg83z84gnmxDouII6Rya6Aymgi/t2I9jz8+EChWc/x6vvxTFKLNb13ZPBUZwRi4i50OA+YhxGLmzDPYyYwx+jZUdLlGGWlFIy2MLbgQB+R/al8OJIFcsvIy9rErIc+HwzciFVthe5+d9O13/9wn5+bvj8iJULjpmFC2ZQZepd9TO5/DAHCz1ZaFB8UJmWMRVnVvFcw4mMKVM3qyFq1FNNd8zxcUA9RNuQmkfcA8ndxbPS0bSRWZOqWVdcd3EIVn/CX5OcKF4FG19R4DcMF43jBOJzQD6fs6FeWDZpmj2l6B+eoWay6OiNo1tL/ij9CjnRvayyzw3ge6N3jsY6gSbKMsbCWSKHNriGVADP93bT8kwd/pM5J6zUIh0gtkr50ncSWD6+2zm5NANDPM3es7LIVr3XniTWYogstSiK5RB+zbIykVXY1NbHXBiUyZyQnq5V4JEEHt6yqKTc8gpl/Drhz8/DMOJ29R8mxq5d5wmUiC86pn3F5OePyesEslpzWQOsCW0a4hAllS1NLMkLvA+IwY+HqXwotrRV3PwE5q8DQxllZi6YsURfkNVAXxU0H/zytBVeWBslGZUE8Ci72snbdXweuAMioTQ5SEnSGpSry+0gXTUWGYXIigOwJ4R2Ri4IPCJEDfxaXyVXicS3BSJ6LyGW6zbO7P/YYziNFBld0SFVthXqqMV1G8kyPCfM0wQeH4UI63fPzmVP1qFichgmX0xHHI7l4nc/P6C+vmOYeyzJlSDJGsnEuqwZte8jpdssy4ny+R1W1sLbI2eNgdEFrBc9OcZrRN3KWK6/ej29d60HLLnVGMuHle1mJalR4cMcq0sz7Drv7HZpdjfbQYc/W1hLPao3Oh3cecWmd/SmOw4D36hXLOGdEUfFoz6f1XQD/HcKzkPfVu5CVKd+67t/dYzgPBLUPY+7cZbQWfJUPQBmBgKFupSYs04zT6Qmn83N2bqPYcSIzp/QLHaW2sEVJMLM2sLZAXXfY7R5wOLwhO2ceuWyVBUnGryFmtVOzo7TQW9bduztSRPC7ScUpoVtLu9BcOoSM/MiSDBWZ28uooWKfAlF6SLaEKQyqpkQlMHWW8aZ8Dgi3wM1U5JrNIRj9tVdB3uuTzWqMW9bucIf+fMpNpiA28j3l0ZK8h/KzjYU1hLwti0ffH+F4XDTPA87nHcqyQVFUqKpqza5oaLwjcuaiKvPeFQON28qmhDYqj/8yD44NpaTRVkpRhsk4A4dfL/x+Z0hPylahUcd1I2ZSkXTZtliJTjLHTkiYncdpGJm84K8qRVnbTUTkGfLSmsLClipr0iX97Mrog4kOQvaR7l9CRsobIyrJfcuwIxx1+zpvLB5uMUgFe1B7n80oxstI8hJGK6qGGKtKk6eyONQJYe3LZQqDqiqzMZDEWToO9VhmYXB7qLKA+JKLvHD1F1hd/r51kS/0KockOE/m/nYtWLTmKhyZiMe/iTai0m7gy3Uk8+WLKS+8cBayDGwkOV9OM2NG/6QdxmnO80+RSMUQMtTuZpc7tm9dx09H3L29w+5hd9WV+MVjurCmuLRIiFiWkbTI84hpqjadG92GptnBGIOm2aFrDxjvLnDLDLeRs8bgoY1F0+zYvpN8vMuyoe/DU46F1jbf30o3xBfwAUFr2JIknGIO8s+QnDy7ZXrnWU6kM39H/ALoO3G5AISlwjCrLyZS4SzTgt6se4J118qP9eBXZILlHY7DiPOpz2ZPuduPq2lPUgowaxLllpC6JQJ+67r/8R6X44VsU2PEMs15Pr/MDtWGnGcZ5Yy+ooJzcZj6FuPYwI6UvaCFd7Pp5le+BMc6Kw3RbArxuSgqlGWNoqhRFJJNbzPf5CrICGCnSUYND+1N1/7ww30eE8QYcX6molRGU0VNh5ubXEYbPIeuUVKdzuOc3cMeZU2W10hiVmZhrM3eBVVTodk3sNZktHdRhKQt45yJewDJyrXR0NgYPInKiItSGS2ldNt7v3/cEzFz6InIPdM8HzU7k5o1XVYKn7ruEILHskyM6J3ZoXWB9y6HcAXv4IoSy1JyZHOFYiwopn6gc297HqTIMcSVWgPyNsViyUV2vWtQWIPFe7yeL7i89sCPb371Gr9O7ovc7TFLVGlOKfMF3FxwhbvOeoWB7wIdgDEl9JcBxyeCu4fzyHKHnzMvBfYWeFE6GPJMFyikZI1ucR0/aa8ZwJlYV9C8u7R2lfp9w5JZo7xcwQUmm1GVL+Sh2XpYQzfeM7NWZDWandsMeyvLPKZmf2oh+UmiUlYFVORLL782OYfezBjimG1OY4gwxSqPyuE1TDiUGfstS8JtxIlRKQW7qfC3iYza6OzlL2EewjcoLOVx682GtyUzAsjhPTOzWovao5gtW2DGDOUFtnCmeV7AdBY2L30P5O3OjnBMkLtV0nV8+YyXD3sc3hzQ7ltKiKwKeOYZtIcR9WsNayso1SMGD7d5xrQ2uWBo9w3N/rmSly4iewO4gBA8tDZ5c9t6z4ucUf56OtRCfj/k+TRW53ERbUy3u5d5v0ong48oazBMaRH8kqWE285PiHvDecDleMHx0zHrrrfqhy0plH/gSkrkua6QGMXQRQxehCOjFJD0dXTslsS7RZe+dR3eHnD4fMBwHMgD3keE4NfgIEYTRN5InAban5p9y/wYjbrqcHf3lpGdmCFuKoI1YmRZXxL5Kf0csvO22cO9aoj0VlYFu70ReXMreRWOjxz6Emrzrevhj4+roiREzp4f4b3nQ7BCMibHPge3JgvKqE7i2w1/JmCNK5Y9gJpGIjBulQ3ynQ/HIRdfIqEDkKW/isxFiIW/UdUEFWC4+7/1u/fLap7j2RyoSXXOaxE+SlFS7oaQS8WIaDgO6E9nQvXmEVCKi/j6SrG29XVBIpWCNNOkUCmZALiOL6i4sbCWpYF3bc41OQ8jTk8nnJ/Pv3mNvwPqZ32wDygSMoyWQoSvy3w4GGvYvIM692Vc4Ax1Z/3rBa8fj3j99IrLhuS0PYi3phDAKhXUhh4kAGSBmeFwmys7YKNfx6rrpptXZDOcWw7+4hcOfrpenbW3wQXMhu6DD9dzRWEjx5gAHaCDzvacX8ZGyqzfctUOAE1Z5q5RoFDo1dNafgbdL2TP68IYWJaK+BsPPnJLc0hxTeAijTr9uthmCsIjUFvJ2tWaU/QU6HOTJHFN1gLowI8pwfGhL5v9MpLlZvaQiGv8pOR1A8A0zFc+76I7Xtiv2zET9pZ1ubzg9cMd7n+4x+5hh3bfUIXOc0jR6FdNhaEXJGSFBGUT3j3scPfuDu2+wdaKeLsBEnsY/GsgwtBlyqlti6AXrOX23iN6nd87QEZtK9Fn673xrYuCfiJ17tleus5E2Um05ZwTfqXQufqLFCeb+cyQzwW62s7oLR10TZVhX5nxRr9K2/K8VW2K/s2hv+1+RRFxyzrsaEzR3rUZ8k9zYtRPrifkwl/SAZUmgpbSHcq6xP2P9wTDx/VZFq2+Zv8O8TuRg3SrRd9+fbIXEo9CZ8c62QeMoQyR9tBi/7C7mdz38HBA5P2EshRIT085ElToldWKqgCAMlTExpKsY43j7y7EK4tycemTQlGCZmxhMlqyzA4TqwiWjYkRyew0El9XNitLCSkVWc76azkiv3cd3hyydJIKzcgNRMwKMVNYVHq1cifuD+3Zbl4y6XCZlnzeCRojPCEpiAFkv5ttEa3EKA20/wrqam2BlIgP0OzIQKisyCzt8nLB64dXnD6ffvMafxe5b5kWVE3J2lCdLXBLt6YRmS38vUlDWzWoLls/SiUJXNvA2mJ1hZIDVYhZwdNNlfAL8TiWmyJre+hr7vQl0hY3dD/iKZ2YJyFkOik0iOsgqXBcHDCzlBQNIW/akf/71q5SmOjyAllmtdddTVV7V+fK0ihN0r8vghjSpggAwKZAdOD6EHJX/a2LDqVVHyzMWigFBhlgkljbmhX255/nOX5zXty1tSsHcCBJpKpIkWLu7rNroHAI0qrf9+xnHSMVT9txk9wLgZmFc3DLmqYe59MLjp8ecf/unpj19Yo8VU21Oq7ZApjXjm3VmoNnngUaRg3kOc9FtNxXuecuoH+95JFS8AGKO56UkNnL8qzTxscdZlcROtHWtEn+Smz115YpLNI8YllGTH2ZVTYkj6WOdQ5r4SozV3LgTDnghsYvDt47ODdjWUY4t8q5FCR8qGAb1D3a/g5N12bffmB1AJSTUO4NsBI+VwtXHk3ptWn41vXYdXh+2GVXtumyprWlSAVAYvKoFG+5MGOXu/bQ8L3S2bVzG0mcNfisFJq5wFvGJb8DooAS7bi4ZkqBu44/IoqSuB07jkJub53xtw3qgsLHZNTmFo9Brc9n4gMwz/gZGXaLh9JLVnh4568OcVEziCZdxha5O2flxtRPmLP0L9G4pFl19SmmbKwl/jEyPkwhwlZryNc3X//bu0xcv+hLHvG4acmcDmkIady3sYhOonyzaHZ1Ph/E+6CsyzyuFrte7wLJJc8Dpn6miO2N2kOKXnmuioK6ezn0q6ZCjAmX1wtZ4r9/xvHpt1ldX70zbvHQTLyTqlUpADUduAKzyiYmbk6ir5e4ybIpsbvfMZmjyk5XYkQhN3Q7n1tG+ruV0Rm6JNIIhWSU1mLxHsmnq8NQbpri2SGl2SngBjMPa0yWoxW84V3Zis7EKJ/dGlUsUkWBi+S+zOwjLfDu9qWWjV+cq9pDmz2dKdq0zpuYFFFyn9zioS0ZJflNWI8LlBkQbuz6MizP8Hr0AbGw1weWDwRxhYhUWiit4L1CGmcswBqp20+r3jZLOUUdsnZp4uYlaWayoW+7w+ACpk0XqDTJXxCRHf/cQjyA8JVc6t9a8zxiGM84Ph1x+nzC3Tuy2iz5O6paOvSLqoA1BaAUAjtseVdgmWbMY0EhVJdxzW/njg+gQ33r4hZZ+tmfBoxnSjQUlIw2zgWeOQvWlihDmYmX2fb40KCtKRFtudHAxlgDBQ0flqxc8M5n//myKSl9LEYEz922TQBo80s6AWFF40QiJZ+fOn95jwyTFonMVrdU7Eq3LqmASpFhEITYt2kYvnTVFMnfrf4dj7sO+0NHhTc3GdouP7P+JrUKyzE3/CUhIYrxlETaSocrcj0ALAEloqjLCELKhw9ADU/SyGQyKTSkqSLGeYGqq9Hd7bB72OPQNjc1O4e6wX3X4a5pEFPKz15KKR/e3q1+FuSVseHu8HuttF49J8Z53esEAQUz9hef+QHQq6OftgbaGx59sP8DNxiKNf6S16Kty8ZKwCoXvWXtH/f07PGeNJyHjCKWTZWRNYCVNBuPC/l9wn8Q/oZlU6nMgxC+kyLXyaolsqhmVEBGaG5yrGrg85eN8kxhKc11V0MbhfEy4vT5hA///h6f/vaE/tj/5jV+9eD3iyfdvlu7GFPYvNlvZ+DgFy74CFNwyIfRqJhxXFQlgg84vFmDNYg3oNnqlEJuZOZZVAXN1LXKna8w4UU/rxSyBnSr3wb/Wkwpz8sxTt/8ECiekSdQEUGdxtptxBiRBuRoWXH6kzhYgXFlFgV+FlduhMr6XoGypYNYxjnHIhMKsobvgKtbz52g+GYvFdkFLyHA8YOnvMctrwDNEEPe1ALPmJ11GQUgQhV9J7lrjQnBkH2y43CW/rXHcOrZ2Wpe4c3t/WGzpaqtkGKJxPp4wwoOpZFfrhhIQ5tiRFlX26+E7o1ffdxvXdPU43J5xvF5j+f3B9z/eI+7H+6xb2vopsa4a1C3NWetVxCb6RA85mWENhbzUGCsJihzInkmO7MRipGyOkTuAxkZUQwxyVl7nF/PGMdzVgBopWGLMkPbAHFZ2rsOd2/vcL/foTAkdZwXBzTfDndTHK8BPOAcFW1zP6HZNQQpN1XubuVdNkEj2pWwllKRNz7Z8H4xdW9T2GkeoUmgk8DpWQa8ka3R59RXfwfApk2Ly+qhW1ZTUuR29iKwK7lZ2NzSeXpG7LKrX0xQKcB7BTUtuYPdwrtbkqt875JCukzEgRKHUpWDqeT6EgI76olMtiiIO9QdOrT7BruGsh/Q//YB8EurrSocmhq6beFCwPFfKEXVO4qPTsxNEcOwINJurYEQgEVGgiqjFttxhFIKSgoasettiL+Qi3sfYBeD4DQAm69fCgJjaf5d1GTuZEv2WWEEUSD1W9bdwx7NrmFzLPpeBbWQ1EUNffXc0rNKZkXzuCEcc+NaVtIs1IghQDM7XwizWpOzaVWX8J4QgHgcsCQaeQa3ugVqkczvidQXfER/POLjf3zET//rPT5/+gnzPP7mNf6uGb9JOvtPb2Hd6CnERFi8spEF5xE2xArF7ENJy1oZqHRoUNJUZBY2m97wTUkVx/TWxdVMP2EliG0hHqkoxWkNIAJZXZS4pfeZncOyOFYGmEyYkwM4gYNkGA6zW8MJOXjVqnggZnyE27k805G5rZAYybnKZG9nU1iWCq3zRLFsDayVt6WFmxbMdYmxoPm3fMYQI36d3/nrSxsD5ddse5+tdgEbCnjtV/02d2dKKahGQfMIYGu4RJ09HSpyL4zVGRWSbkgSuGiepvLGSy9YhPfyrCw581w6aKWxYmRq1ULfssbxhJQi6nqP8/M7DKcBbnIwdwT1ySy66mqSz53LbOCRORFpDaihTr6nTkXr1WBoM6oSWStZnC7ozxcMwxHT1MN7+l6tpdGCVqtKotk1ePPHR/z44yPumhaz9+TueB6A5ttnvaawKIqCWcme4pRfeyI17gmGJz26GMYoBG+uSF5bh76yodGIJOdluaZ8V1fv8qoYWKY5FxIi3xJpryTGKa1zoQ+sfiDA9UjgW5eQUeXZJcWQIJsE4QoP4erz5zFMwMJGQykmjOch733i8y/dr4y7ZP+SQli6u8QJiWJ/nC2aZe5bWuac1JlfU9jboG4XqLjc1zV+vLvD89tH9H/oc8jS1E+ZeyDGUXn0GBMC1iZsbRgSW4lvzwWVicDZGyMjAQHamOzemn3omawtEcmlyFiNzt12cJ54YDcqud7sdhiXBZc9RYT3xzKbBM39tCYEmtUzYGuxLORPMecCaORNAV8Rfinp+bUmG02pkvfEElBs7pURISZYyj8pJVRNiXbfwhakmHn99IpPf/2EDz/9Fa+v779KaP59d2ZTnW7NOiru8OWLlxdzZmMRU/irilzY4VKF0/+u83GZCUmXQJuaYetRQhnUBtIT1rxURH5xlGjlQp7BCrv9VqLHPIsTXUBid77CWJTW5Ie/LyxiTEwoQ/684qYHo2FLledAmrth8WBXHHoinXOu7BM2Zj9kyiDe7FvOgLYGBWuMi2nB2ZBFrCwfAt4U3z7rFIkUQBU8SbSowyvqkOHKlETHGvIsVnSuYnghmuuyKTNbfQvfS+SuoD9bRYcgIUJ8EpleSolefL0SOvONwzqquBXuXdjEY5rOGPvhSlZUWYuuIR7G7n6H/qHHeLmD8wvG8QKkCO8XTJNwP+i+LONCRSxHi265Gtt7AfAzl8Qz38AY6ohI2lWhKCueY1sc3hzw5s9v8ce7e1hj8Ol8Rj+MOH06Aj88fvO1l3VJ3/eywDm6pvNzid19lwmNWm9CsQCkuCAx5GkMSbUkn90WJhdz8t/oEFt/JnF/iLgoyp+tHa3j3A+6R3pzYMi9XM1eCAnDzTN+CdoSJ77xMsLNLh80gjqJpasc3nI7hB8DxPX79NfohUhzhd8i90CxGZNA24J4bZ0YZaQqpldFXTDfhEiRQuq9ped9vlzw2HU4NA26qsKbHSlb+lOfnUJjjLnJCczwz9+71bmwvXrHtyIOLgpJh84qLS6ytA/52RFERLM/BCEmq333Fs6XXISUVrL4LUvCtIg8aDOB0C2E3Owf97l4lUbOL/FqX9OGkjuFvyUosIxLiCdQIHYVqrQSx5VCNh6TYCZ5BmXcItp9W1Js8tRPOD+fcfz8ipeXn/D5809fv8av/YYVvorZMQ8ASq545IEX2Q/d+MQ36ueHLcUthgwTytpCX/L/S0eQUsqVFf0aH4qJmKZigyopUHL41F29hsTc6GMynUcUDBk5Y1BYi8oqWL3O/sW5UAKJtqlTwu62tb3SgltO6BMinrDfAWTnv3mcr5jdAiHNwwzvJd5SXzm2yazJyQyZjTfw53fffO2yuYstrWxY3nmU8ypHkcLFWM2Ss7TxeKfwlLIufx4ko1aobPV6j5nBKs8HVby08c/DhHmk4o6Y3zZDxLh6npBJQbcurTWcWzBNA6bpkiVlIUWUHKazf9ihP+4pKOQ8wnsqFrxfILKbLEMSS1p21ZMiT3EXJ4VA4DhSIakBgNH2arZf1x1HBpOc6P6He7zd79GUJXykhMjz5zM+//QM/N//2zdfe3fXkl9BzwYkUw+lFHYvOxze3uUcAjmcM2ET9F4rJYWXFD5YEasYYdhq+JeWEIRFNy5+GMILsmWBkg86kf+ltKaBCuFOG5MP1G9dlIWxCZiZSI9NYxq9Xhsf+nlkxYt4BuEqh0Q+m2OjKclZ2FrdZiMvNkITT/etda14CQhXRkhiyqxy6sk5GK1xi5L/w+mYD31ryBBs39Y43+0wnsa818vhTsitWtE8zmtRSqH04q0RsbUql0JfRrz52fDrnH6NGF9HgGJP23IWhi1sJvsGxzNxLkKKG4u+4zDAxwhJhhQSo5sd+tOA3WVCe+hyeBXtM9yopvTFGabzqEO69ehDRnGlGAo+5kJYfPvHy0hcn8uYMwBI/VLTnwfnerAt+DiSI2jfv371Gr+6Ky7jQgEDZZGzhlNKxJZXFpJHLTCWRFMKzC1QVtpAXiLZ2EJV24S1PO8taJZjC4O0gZJTQr6Jnqtosckcz0M2f2l2DZzIf3DbyX9+vTCkQrCb5xtORKN13EDVasR4GfN8K3tvs8mCHEzysFiRGYIh+URRvgtDVmQBO2BgX3YhyclDbgqbzTrk75SfUVQFeclz8XDLwd/sGmijMQ/VVXXrBtqUSzYlWrsb/u54rJFdrpgTIrPMrR71yxV8gHIKQQVEhgmlO5LrlzwA0a6KSVNUcTXy4BfRlhZYvvnSAVAu+TwPWJaRTDlORE6cFge1U9jVNQ6HHfrHAf2xzwZVKSVMU09dkSWjjqIize3+YUfMfnamFDhcnv8YyItfHPmMNVBnTXwZNyOlmP++oirQ7hvc/3BPAUhFgYSEyS04TSOOn17x9Penm6794Q+PWGaH0+cTnJsxDGeEGHD6fIe3f34Dpe5QttcGQcaYq2hU8V6QfQEAZi5wfp72uUEOeGTnZ3clYxR0UXPqYFGvB4wQZhdGxahDjl+FPH9tTW5tJCjj3SGyxa5mP/3soIcIvxnbyPVunTaBTcyzzLm1ho3mqgGSTlBg7OxUKnJYRrxkf4hs8BKFJOp55BkC+nnGt2M9wId//4jKFqiLAm/2e1hj0JZsOtZWsIXJEDaAjXvntUxT8V6gDPEVHMGzLPsEolIwm9EIsDaGIl2THIaSOSJ1V6PlcZPsewLxjxfaL1NK2D/sshPgt673Hz6THwDzGAw3N/M4YewHlHWJhx/vqfFgi1yfi3UhlkbESHk2WisKl0prRLgyEUJCJcnihqzNEvjzy4WS/+YhO7QaQ+NRy4RCymcIWX0l++r2ffql9dWDfzwPiL7K4SkyOyuMQVuSwUxKFCuozyOcC0Dkh5/JOVtrVnl4pXrPD0p2W1r93AGeMxsmkG2iEqVrlISm4Tzi8nJBf+r51xOaXYNlnG/WsQPA5eWCFCI9RIry7SOPPHyI6Oc5wzJZkjMua/WvSA2wjWjdvtCSbCg8hxgid7bzVV6BwMzUCc2ZCdzu23wf4qbgEIb4cB5/5hfwe5fogKnSLlii47PCwy+eyDUp8fxKijzaAKUjW+eaERIZ+qVlM/0Gnu/xfQh+hW3dvOR7Qjpimu2Tf/w6HrAcRUxeAiVL+267/vv7H3E6PQEpkSMXF5bjMCHcR3RVhceuw/D2jm1FryNHl2Vm1zZL0Zkl22vu2zWB7Asjm+gDlCY1zVKRjI70y5YPHk3+3NwRHt4c8PiHR+wPHUpr4EPEZZrx+pHIPh/+8v6ma3/757cYzwM+/eUjlnnE0B/h3ITd8QGX1x6Pf/S0AfPsdf0e6FqWcWYCK+v8gasDLl8vQ+XbQnBLeAvOwznyYgcAXVaZ+1KU67jEs4RTZrzK0TPh59vc22bn1uyF84B56hGiR1HU2GO/ond1mQOigluRqm1Bk/NMNHnya7MpctL1v8tcf2vuYozOzY4QBcfLiHkeobVFCJZVQpJOFzEvDv0y4F/v9t987X/9f/4VSqtst66UQslkOltazulI0OD9G8hjx5QSXIyI8ToRVThCOUgHuDrYM0kurUZVSilYluuVTYWaPTF2D+Sv0NQVGaYxMnU5XjCcBiZYx5sNfJ7+9oT20ObwISIuUzE/TT2qjxX644C3f36Luqvz/gdwqBKjX1qvY57cFPPXrbWG1/RMB+cBtWQt/9QTF2jqB8zzAB84qrdsoJTOskCtdS5sbWlRlg2qqkXT7P75Gf/CL46tCnqx5lVDLMlvADDsB/KjH2YEL+ldP3+wV0hLI+U57hryk2e/mkNneNZTNvyy1ysrNvp1/nZ5OeP0+YThtCIP7aGlDiBG+BvZva8fXxGcR7O0UJpkhTFGhES2ohKl6Caqwud+wniZcoAKXavK5Cbp9mR2LS86wFwFrtyFDCZ+1W6Z4YMjy0cmeZVlTX7tMle1Bp5fBKUUW4euHfK3rvu7PRSTZs7PMtsUNrGH1z7b6xalzUoGx/Bs1dVkU6zWlLGt1lmeBUGDgOtELSlmMn+DD/2UErsgbjTRWgFGo0KVN0jvyGb0a9Xvr60ff/yv0FpjHM4IwWO4nHF6PuP8csHyg8dd2+KuJSKd/wN3pRvpDbA+/7/0GRQrUkRrL/dIAknE0EWkbwQdcuBNRUjP3bs73L27w0PXorIFFu/xfLng6W9P+PDvH/H09Lebrv2HP7/F68cXFHUJHzyG8Qw992jbTzg//xHjZaSup6wy1CyFGF1LRJQ5fUQuRHNs9gYJ2L4n23juECJ720vin82Qb1GVmUfjl/Xey4wfoI3v1mdfQsXGy0jf+/kZMXpYWyLGR1TN6o4oaoOrLhjCe9la8BJaqcxqNSvXSvfsOhNFcODtuyOfaR5GLPMEW5SwjvfmiRoQx/vR5eUM3HDw/+X/8e95PwGAhx15vpeb0CfvPVRYOTSCBkozp63PRMQY1rAsIYgD9H2HDeolr35iObbI9XJa6eMed2/v0N13qMUsh5GPy8sF589nDOce7b7LfINb1uvHF2ij0Zr2an92bkbfH1EUJY5Pf8A8zmRJXFhSzwC5cZNnUa5H/le4cEuYM0oge5+fCWUaLj2m8YJ5GRFj4EO/phyPukR3aNEcWhqtMv+hait03R77/SNiDJjn4Tev8euWvYGgF8/wkszcYowoiyJnrh8fBpw+n9C/9llmBX7wt2YVoq01xQp7ySG43fRlTi5mB82uyW5kIh1b3ILxRD/39dMRx09HjD1dsFIKd+/I6jHEeHPX//kfn5mQE1BWBXVkSrE5jrhZEbw582E9Xsj4xLslb+rmUqCwJYVwmDXcQWBPme1S90CezwIzey8b6PrSWFsghA5lUaMcS1i2tk0baWNm4t9Y9Lw7HFBa6tjPz2cUzEDNsGeMCJ7cuMq6hGH96jItmIYZ1YUkTMJC9otoXJefzV6F1KT4ednCVXJvyNUqZo1uWVMhuDVGIShW5S7gytb5G9ef/tu/AgBeXn4iEs3U4/R0xPHpiNd/HfBmt0NTlnjsOjjPqZLjjGlY5TzOTYiRCiThaWhL0Oxi1+sUhCzFmGFLKvwWJnIGKHCMKUuDml2Nw9s7PD4ccNe00FrjMk94ev+Mj//xEZ8/vcfx+Omma/+XN2/w4d0nNHuS7zk3YVlmVFWLl4/PuLz8AO8C+RrUJXLMqL3OnnDs9Z/TKL849OV5B4jAuN4PhjAj/ZrRFlVTZ8MSsaxNSbwbwvrP4vi/R0zDb8uafm1NboXT+/6E0+kJITgURQU3/wnG2rwneedzNsQyu6uRnuxpIlOUdfW9a+Q/I/yoGCNUWGfG3m2y54cR8zJicYRkOW3hlyoXH8N5wNRPNOa5gd/xt7/+vxC5mDfWYP7TW3YQXYm2bhL5XMwFjhR3mbC8KQjc7K70+0oRAc8EIgkmRj2lANj6u5RNid3dDofHfe70AWCaF1yOPY78TvbHHs7NUKrLRjm3rOOnI9pDxxp5zR4OdN0UmPWM1w8vOD+fcffDPe67FlWeudP3NOs5P4NSEG2Ny/La3Dt673tc+tec8KeVRlV3lNa536G773D/4wN2dx3xyXTkkV+Lw5sDpukPMMai7/9JAx+dZ7spV1fjZUQ/k8ymLUsYrXAcR7zsX3EqySpQ2Le2kFzwlZF65evNB/xK8kJ+wMSJqu7q7JBWGNrcJ08EiNPnE17ev+D5H59xOj5jmnvqiooCy0QPmw8BPobfKWG4Xh/+9vc8t+3uWoQQYbRGadfwG0mE84vHPC1YFprLiFkJVcVsa7vhGiSkq8PNewqU8W7B4iZO81quyHCi4a7rDtaWjALEDYciZlObGFKeE9+y/nB3QFuW8CHg9LBDs2uysYX3DsYwG3USJYbKaXjzwI52XOR4NqNYpjmPeb54/vOhv8q9VuhYljYmz/mEXS4HYd3W0ErhbA3Gy5RfqOIGRQMA/Ov/QQe/MQaX8wtijDizJeb51GO4X4jrUljctS3O9zs23RkzJ8M57o5ApjzK6DyqyPGhcijyd+imJXMzhjNtZvQ5iqySqJoKzaHF4e0B7w4HdFWFfp7x/uWID3/5gI//8RGvrx8xDL9t3flr6493d3j8wyNxByrqoMbxjOfnn/Dp01/x7v0P+OP//kc8/vhACZCsqf4ydGqAeC8kkOpO52sNAFSkd0MS61IStY4gHdS5lRU5EoovuXgCCJk0CmN+Q54LIX5Vz/xra3JMLhxJ0SAJe9aW6F//K0IIWUsNLmJylsDGLVKea2ulUEn5+rcFkFw3AOhE/yfvDYGUUtNlpKyThfaGEBzLni2pXaYF/XHAMi44Ph3x/v/8cNO1v//w7/DBM3mUYrn3j/tcuGwP8yyb5P1dzHuCj5nAJzbuX5ofCQGY+E6cNGlVHoGKtLnuauryd02Wv00zxV2/fnzFy/sXHD9R3LVSZK6zu+/Q3RhS9PSPz9g97NHdd+jYxKnualhLnJa+P+Hl6TNePrzizZ/eAncHtGWFwIe3eNvkTBF+FrfSRlmClgjbf56HnOSYUoQpG5RljXa3x/5xj8PbA+5/uEfd1RgvE1JKmWsl6IG1Jaqq+c1r/OpZWHd17nI9H7bDqUd/GeG8R2kt2qrC2/2Ev7PUZ2Lpi5j+KC0mBWvFSKYURJwQTbfA/RJPK7O8qqnQVCUKhm6kGu+PPV4+vOLpb5/w9PQPnM/PWJaJblS7zwd2SPFnFuK/d338+O+IkZwJH358QEqJpFwVzZc+1yWZeTCRR3y5Y4wIUXK3Q678xc41JYqYXXO6A2IMcG6hF9rN+b8DlL0ssZ116nJi2xYFoG6foKY88y6LmwoeAHjodrDa4DJN+MQuglVXw5wGwE0bWSZvvhEIPOeWYAvia4ht8QLnZjg3X3/uzfjHmAJV2aAoqzWMg0cikvJHMa9t9sqvuxqHrsGhbtj3P2SWrWLntFvWv/3f/g3WEmfgw18ajOMFyzTj/HzC6fMJTw8HACTts4Z0z/39Dns5+HNqYI95GZEuqxkIQdVsWhVWKRDAWQTjjGkasmmPMZzVXhhY5i+0+xaPhz3uGnoWnvseT39/wsf/+Ijnpw/5sLplPe52+OPDPR3+h7coywbOzTgen/Dp03/g01//Ba8f/oR3//oOj7sddpVGUxQr1J+Z3Nd2xFfjHc+ojgdSWjt9WbQpGhRFeYX6CdSvNLDwfcsZIfyciZeCc99u2gUQR0Gko/M8YBzO6IcjlNL4/PR3/Pn4Z9oL2gpVRZLSaSAFDunzN9IuLamGJs/8I4jgBh6Jbv3rI2g8ovge+kUUPiMfCqS0oL+LUh2DIz4PQCPDlw8v+PjTf9x07c/PP8F7R81FSQmAb//0Bt39DjGE3ImPzB8KwcNayyNMnZugbShPtnLeHHqGmzjZ902BfOiXteTM15kbZQsik4/LjMsLBUC9fnjFy4cXnI+vcG5GXVOn3t3t0Ha/ffj92vr4/j/Q7lvO52hRdxV2dx267g5lWeN8fsbz83s8v/8zLscLxj88oqsqtGWJnj1YxFZZuB8iR90+F0oByaxkvBA8YlqNjrSu6HqaPX0etmLe3e+y8Y/kgRirsXvYsZNoideP/+TB3+5bgkzVGrhwfrng8nJG/6c5y5re7Ha43+9wvGsJ6pbc6mVjt6g1bLmG8ZjCZGmTPCASRFG15INelTROqLhrG5cF07zg/PmM5/fP+PyPJzx9+juePv8d5/MzQnDY799whjS7zm0kZN+6np/fQymDuu5weX0LPzsU1uKubaC1xsfdCWd+4AHklzE/4EoDCCtUHyOcJ1RA4HzvFoRILwoFmQT+byF3+WXVQFfcBeuV5CgKAukc+UNQFS3EwV9gz/+e1ZZU4e6bBvtDR4llT3uM55E3H0oVI8tVkyHsGLkD45/rF4d5ppnkwn7t5L4Wr1APQjMqeL+gjh3K2CClIjt62cKiqkuypd015FR3v8dj1+Gh61AXBU7jmFEGw/NBCVL51vV//Nd/RbNrmFdi8PE/PmbyzcuHFwrneTfjsSPIvyqIZX94c7hOB/QO09xT4bDM2Z5WIlq3zwYA+ODyqCim60Qz+XdbWvpZTQOjNZ7OZ/z9wxM+//0Jx4+vOJ9fsCzTzfyGpizxZr/Hw4/3ePjxDfZ/ecTnz3/HMJxwOj7h46e/4P2//wk//Jcf8bDfoe06GE1ZEhKdHPz6HkzDdTDXltfhlciEFSiTIUGpMkO+Ettad1W2PS7q4jrfgMl987h2w/9MJruEs9B347M/Q0oJnz79Fc8//e/4w3/7EVpr3LUt2YfznF3kzXneLeoWJunR9ceV1JzoPZexYEYDmOG+iBtcPvRDRg5JWUQz3eNTwuXljGVZ8Pr6AZ8+/fWma+97OkSrsobRJo/N3v75DaeMmtzVumXGOJ2hFCURllWVD/oYAhKkMLvOF1l9Wta9XzE6KQ1f3dbkjCneBDHSGOMy4vUj2Wi/MOQ+TUTqruuOyLNNiboobrIs/vTpryhLQhnafYtm32D3QO/Cy8sbnM/POJ8/4/mnZ7LTnhdgRw1AVRL/xtprnX/OKWFLb8g1ezIYy5JfW6Fp6H4VtkTd7LC/36PdN6i6Gru7jkjLLqDZNegOLR7vD2jKEq/DkFHWbCz1K+vrB/+h3UTMppxFfno+47nvMSwLDk2Du7bF2/0ez48HTP28al9HktcseiXZCCHLbglaG7ifuroGu7rKZjkKCrP3uMwE7z//9BlPf3vC86cnPL+8x8vLe1wurwCAqmpzdRmcx+wd+nnGLVlVyzLhdPyE3e4ep89/RH8aMDuHwljcNRrvDnucdqfcYaeUEKLnijyyyYlB5H+PMeaqLiXa8K8y2WMgOBTSLVAmd13v0LZ7VFVLzm2moAJgoxOXedEWKhPi3y3LGoOuqvDQtnjcdXh5JLjp8tpTR+Ro1g+Q4YgwXGWDF3WBUgrOScQvd/opIqaV2Z9SRNIGOq4SMGL9mixbzPpd7gAeHg7418dH3HcddjV5NlymiZPF2F5ZqTVI5BvXf3v3DnVRZFe14AKOn45IKeHycsFT8QnzOMP/MeDNYQ+jNSpLh797e1i7tGGG8wsogpXumVYL5m1BlmgDp8o/cMfK99bYfACJ1bOw+lNKeDqf8b/eM7z/6YjhPCKlAGMsEUBvWIUxONQ1qwYe8ObNn/H8/A84R3Dk09Pf8bf/91/w7l/eURJcSYhcaXk8N1bwrkWKyO80yeJ8RsXExGWFiDmbfjMCNIZ8zGsOJMk8H/4zNIJkpntPfgsyMtPaoixum/MO5zHnAUiMLkAEr9P5GZ9++gnP7/+IH/7Lj8DdAXdtg+UPj+xuGXF5OV/ZcscQ4fGFVbE0O9ZQrgiT/8SuV7zaCSmbCD3cRPh672BtAbcQOiSjxHmZ8Pr6Ac/PXzdy+aUVgsc09Xh5/QBblIhp5TLdv7ungk2IqMHBOdq/nFvQxn1mnyudSLaXPD3LzNqj6zYcLWuz7t9y6qoUd6YwjKayi+O4YDwzp+vjEZeXM86vF8wzXXtVUZcuQVjWmJsO/s+f/wFjCnTdPZpdgx/+7QeUTYmHPzzi/v0PeH7+B5ZlwsvLe7x+eKFG9z6gNAZVweRb9pnwO0I9xQcgIWYkZLvPFUUFawsURYmUiEwpMvD2bpUvSjKjbS0eHg744/0d3u4PqKzFcRiglSLJ9/jbSqavHvzNriGd/mXMesvgI+Z+wuvrGU/nE/Z1BaMU7tsW9/f7zEYXTS2xF8ngJZQWNpnsbERGFauTmdYKRV2iqyrUBWW4+xCx8KF/frng9HTKwSnn82ecz88Yxwu8X4ggBHX1snpHmtY3N3S+1ljMy4TL+YUfuFd8OB3xA89V75oWzZ6CdIq62FSytEjOZVYCkwpQquHN3aMotml/9Hmlo6fc5hJl2ZBhS9XwdVkeZxzQNLvshqbZwEMOfbHTvFXLDCAjOl1V5azxw9sDgvMYLxPFk8oGx50o6Vt1htjnYWaLVUlftARRfpFkZ22BqiJJSlk2HNFK87WaM8a7uw67hx3u393hXx8f8efHR9Kvp4RpWSifIF57BNx6/fctzQhfhx6nPzzi/HLh74dml+NlyvyK4GgmKgYl9NLW2N13NPpyC8+wNzpbPuy/lDZmvbjwQtQqdxI3RFsWSAl4ulxo5PT3z3j58ILL6wUxBp7ztShuPPgW78kApmtw98M93r79I56f/5w3+Xke8fnz3/HT//wT7t7doahKPOyIC6AVjVeEoxPZDMXXPkszxcQrsE56y/lQilREEk8t33/VVGsYGBMh3UKqnmmY1uS/uMKltrjNr508GWhkVhYVP5M1F+ukcvj89884fnzF/n6Ht/s9HroO87s7ljL61UkuCty7mhZtJa0ZzTEaKiYaezDE7xcH5+jAl4YBIFSImouAwS1YlmmdFTMB7fcYufzSqsoGzlOBdzp9hjGSghoxnga0dx2puxx1sHRPIpZl5O8mcu68hS4UUqrg3EKGNYxY5sTC0uZx71auHdjBNXJWg2FuTH/s8fz+Gc//eOaxCiHKdd2h6XboDtTtQ6mbCd3n8zOaZofj8Qmf//6AorTo7naomgqHNwccnt7ifP6MGANOn+kserrrsK9rhJhy4+omx4mZSyY5jyeNZVlywwQQd6esK46bL7I0VnhLORCMC31tNP7w7hH/5e1bPHQdHrsOVVGgqyq8DgOeHnZ4/fDym9eo0m+0g//jf/yPm27c/y+v//7f//vv/r3/V7v+/8zXDvznvv7/zNcO/Oe+/v/M1w78577+X7v23zz4v6/v6/v6vr6v7+v7+r/Wuk3g/H19X9/X9/V9fV/f1/9fru8H//f1fX1f39f39X39J1rfD/7v6/v6vr6v7+v7+k+0vh/839f39X19X9/X9/WfaH0/+L+v7+v7+r6+r+/rP9H6/wBEXr2ATFBbywAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 648x288 with 24 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 8, figsize=(9, 4),\n",
    "                         subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                         gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The results are very interesting, and give us insight into how the images vary: for example, the first few eigenfaces (from the top left) seem to be associated with the angle of lighting on the face, and later principal vectors seem to be picking out certain features, such as eyes, noses, and lips.\n",
    "Let's take a look at the cumulative variance of these components to see how much of the data information the projection is preserving (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative explained variance');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The 150 components we have chosen account for just over 90% of the variance.\n",
    "That would lead us to believe that using these 150 components, we would recover most of the essential characteristics of the data.\n",
    "To make this more concrete, we can compare the input images with the images reconstructed from these 150 components (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Compute the components and projected faces\n",
    "pca = pca.fit(faces.data)\n",
    "components = pca.transform(faces.data)\n",
    "projected = pca.inverse_transform(components)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x180 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results\n",
    "fig, ax = plt.subplots(2, 10, figsize=(10, 2.5),\n",
    "                       subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                       gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "for i in range(10):\n",
    "    ax[0, i].imshow(faces.data[i].reshape(62, 47), cmap='binary_r')\n",
    "    ax[1, i].imshow(projected[i].reshape(62, 47), cmap='binary_r')\n",
    "    \n",
    "ax[0, 0].set_ylabel('full-dim\\ninput')\n",
    "ax[1, 0].set_ylabel('150-dim\\nreconstruction');"
   ]
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    "The top row here shows the input images, while the bottom row shows the reconstruction of the images from just 150 of the ~3,000 initial features.\n",
    "This visualization makes clear why the PCA feature selection used in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) was so successful: although it reduces the dimensionality of the data by nearly a factor of 20, the projected images contain enough information that we might, by eye, recognize the individuals in each image. This means our classification algorithm only needs to be trained on 150-dimensional data rather than 3,000-dimensional data, which, depending on the particular algorithm we choose, can lead to much more efficient classification."
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    "## Summary\n",
    "\n",
    "In this chapter we explored the use of principal component analysis for dimensionality reduction, visualization of high-dimensional data, noise filtering, and feature selection within high-dimensional data.\n",
    "Because of its versatility and interpretability, PCA has been shown to be effective in a wide variety of contexts and disciplines.\n",
    "Given any high-dimensional dataset, I tend to start with PCA in order to visualize the relationships between points (as we did with the digits data), to understand the main variance in the data (as we did with the eigenfaces), and to understand the intrinsic dimensionality (by plotting the explained variance ratio).\n",
    "Certainly PCA is not useful for every high-dimensional dataset, but it offers a straightforward and efficient path to gaining insight into high-dimensional data.\n",
    "\n",
    "PCA's main weakness is that it tends to be highly affected by outliers in the data.\n",
    "For this reason, several robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components.\n",
    "Scikit-Learn includes a number of interesting variants on PCA in the `sklearn.decomposition` submodule; one example is `SparsePCA`, which introduces a regularization term (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)) that serves to enforce sparsity of the components.\n",
    "\n",
    "In the following chapters, we will look at other unsupervised learning methods that build on some of the ideas of PCA."
   ]
  }
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